diff --git "a/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Submodule.LinearMap.sym.json" "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Submodule.LinearMap.sym.json" new file mode 100644--- /dev/null +++ "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Submodule.LinearMap.sym.json" @@ -0,0 +1 @@ +[{"isProp":true,"kind":"theorem","name":["LinearMap","codRestrict","_proof_1"],"typeFallback":"forall {R : Type.{u_4}} {R₂ : Type.{u_2}} {M : Type.{u_3}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 : Semiring.{u_4} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 : Semiring.{u_2} R₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 : AddCommMonoid.{u_3} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 : Module.{u_4, u_3} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 : Module.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26] {σ₁₂ : RingHom.{u_4, u_2} R R₂ (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11) (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14)} (p : Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (instHAdd.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (AddCommMagma.toAdd.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (AddCommSemigroup.toAddCommMagma.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 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Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x) (DFunLike.coe.{max (succ u_3) (succ u_1), succ u_3, succ u_1} (LinearMap.{u_4, u_2, u_3, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_4, u_2, u_3, u_1} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 σ₁₂) f x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.124) (h x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.124)) (Subtype.mk.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x) (DFunLike.coe.{max (succ u_3) (succ u_1), succ u_3, succ u_1} (LinearMap.{u_4, u_2, u_3, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_4, u_2, u_3, u_1} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 σ₁₂) f x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.126) (h x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.126)))","typeFull":"∀ {R : Type u_4} {R₂ : Type u_2} {M : Type u_3} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring R₂]\n [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n (p : Submodule R₂ M₂) (f : M →ₛₗ[σ₁₂] M₂) (h : ∀ (c : M), f c ∈ p) (x x_1 : M),\n ⟨f (x + x_1), ⋯⟩ = ⟨f x, ⋯⟩ + ⟨f x_1, ⋯⟩","typeReadable":"∀ {R : Type u_4} {R₂ : Type u_2} {M : Type u_3} {M₂ : Type u_1} [inst : Semiring R] [inst_1 : Semiring R₂]\n [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n (p : Submodule R₂ M₂) (f : M →ₛₗ[σ₁₂] M₂) (h : ∀ (c : M), f c ∈ p) (x x_1 : M),\n ⟨f (x + x_1), ⋯⟩ = ⟨f x, ⋯⟩ + ⟨f x_1, 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{R : Type.{u_1}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20] {f' : LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32} {p : Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32} (n : Nat), (forall (x : M), (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32)) p (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11))) f' x))) -> (forall (x : M), (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32)) p (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11))) (HPow.hPow.{u_5, 0, u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) Nat (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) (instHPow.{u_5, 0} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) Nat (Monoid.toPow.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32) (Module.End.instMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2096484510._hygCtx._hyg.32))) f' n) x)))","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {f' : M →ₗ[R] M}\n {p : Submodule R M} (n : ℕ), (∀ x ∈ p, f' x ∈ p) → ∀ x ∈ p, (f' ^ n) x ∈ p","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {f' : M →ₗ[R] M}\n {p : Submodule R M} (n : ℕ), (∀ x ∈ p, f' x ∈ p) → ∀ x ∈ p, (f' ^ n) x ∈ 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[inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.11 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.14 : Semiring.{u_3} R₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.26 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.40 : Module.{u_3, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.890229545._hygCtx._hyg.26] {σ₁₂ : RingHom.{u_1, u_3} R R₂ (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_6, u_6} M₁ (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1736679977._hygCtx._hyg.23 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10))) p p') -> (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4)) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) M (Submodule.setLike.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10)) p x)) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) M (Submodule.setLike.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10)) p' x)) (Submodule.addCommMonoid.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10 p) (Submodule.addCommMonoid.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10 p') (Submodule.module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10 p) (Submodule.module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10 p'))","typeFull":"{R : Type u_1} →\n {M : Type u_2} →\n [inst : Semiring R] →\n [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → {p p' : Submodule R M} → p ≤ p' → ↥p →ₗ[R] ↥p'","typeReadable":"{R : Type u_1} →\n {M : Type u_2} →\n [inst : Semiring R] →\n [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → {p p' : Submodule R M} → p ≤ p' → ↥p →ₗ[R] ↥p'","typeReferences":[["SetLike","instMembership"],["PartialOrder","toPreorder"],["Subtype"],["Module"],["Submodule","module"],["Submodule","instPartialOrder"],["Membership","mem"],["LinearMap"],["Submodule"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["Submodule","setLike"],["RingHom","id"],["LE","le"],["Submodule","addCommMonoid"],["Preorder","toLE"],["Semiring"]],"valueReferences":[["Semiring","toNonAssocSemiring"],["SetLike","instMembership"],["Subtype"],["Submodule","inclusion","_proof_1"],["RingHom","id"],["Submodule","setLike"],["LinearMap","codRestrict"],["Submodule","module"],["Membership","mem"],["Submodule","addCommMonoid"],["Submodule","subtype"],["Submodule"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","domRestrict'","_proof_3"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} {M₂ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11 : CommSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 : AddCommMonoid.{u_3} M₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 : Module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 : Module.{u_1, u_3} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17] (p : Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (m : R) (x : LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24), Eq.{succ (max u_2 u_3)} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.domRestrict.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (HSMul.hSMul.{u_1, max u_2 u_3, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (instHSMul.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (SMulZeroClass.toSMul.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddZero.toZero.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))))) (Module.toDistribMulAction.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))) (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (smulCommClass_self.{u_1, u_3} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (DistribMulAction.toMulAction.{u_1, u_3} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)) (AddCommMonoid.toAddMonoid.{u_3} M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17) (Module.toDistribMulAction.{u_1, u_3} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24))))))))) m x) p) (HSMul.hSMul.{u_1, max u_2 u_3, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (instHSMul.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (SMulZeroClass.toSMul.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddZero.toZero.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddZeroClass.toAddZero.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))))))) (DistribSMul.toSMulZeroClass.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddMonoid.toAddZeroClass.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))))) (DistribMulAction.toDistribSMul.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (AddCommMonoid.toAddMonoid.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))))) (Module.toDistribMulAction.{u_1, max u_2 u_3} R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 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(CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20), LinearMap.{u_1, u_1, max u_7 u_5, max u_7 u_5} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (LinearMap.{u_1, u_1, u_5, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R 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(CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_7} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_7} R R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_7} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (smulCommClass_self.{u_1, u_7} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (DistribMulAction.toMulAction.{u_1, u_7} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17) (Module.toDistribMulAction.{u_1, u_7} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_7} R R R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (smulCommClass_self.{u_1, u_7} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (DistribMulAction.toMulAction.{u_1, u_7} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17) (Module.toDistribMulAction.{u_1, u_7} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24))))","typeFull":"{R : Type u_1} →\n {M : Type u_5} →\n {M₂ : Type u_7} →\n [inst : CommSemiring R] →\n [inst_1 : AddCommMonoid M] →\n [inst_2 : AddCommMonoid M₂] →\n [inst_3 : Module R M] → [inst_4 : Module R M₂] → (p : Submodule R M) → (M →ₗ[R] M₂) →ₗ[R] ↥p →ₗ[R] M₂","typeReadable":"{R : Type u_1} →\n {M : Type u_5} →\n {M₂ : Type u_7} →\n [inst : CommSemiring R] →\n [inst_1 : AddCommMonoid M] →\n [inst_2 : AddCommMonoid M₂] →\n [inst_3 : Module R M] → [inst_4 : Module R M₂] → (p : Submodule R M) → (M →ₗ[R] M₂) →ₗ[R] ↥p →ₗ[R] M₂","typeReferences":[["smulCommClass_self"],["Subtype"],["SetLike","instMembership"],["CommMonoid","toMonoid"],["Module"],["Submodule","module"],["LinearMap","module"],["CommSemiring"],["CommSemiring","toSemiring"],["Membership","mem"],["AddCommMonoid","toAddMonoid"],["LinearMap"],["CommSemiring","toCommMonoid"],["Submodule"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Submodule","setLike"],["DistribMulAction","toMulAction"],["Submodule","addCommMonoid"]],"valueReferences":[["Subtype"],["SetLike","instMembership"],["LinearMap","domRestrict'","_proof_2"],["LinearMap","domRestrict'","_proof_1"],["LinearMap","mk"],["Submodule","module"],["AddHom","mk"],["LinearMap","module"],["CommSemiring","toSemiring"],["Membership","mem"],["LinearMap","domRestrict"],["LinearMap"],["LinearMap","domRestrict'","_proof_3"],["Submodule"],["LinearMap","addCommMonoid"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["Submodule","setLike"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Submodule","addCommMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","subtype_comp_restrict"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} {M₁ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.23 : AddCommMonoid.{u_6} M₁] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.36 : Module.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.23] {f : LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11)) M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.36} {p : Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.32} {q : Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.36} (hf : forall (x : M), (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2791627020._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_6, u_6} M₁ 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↑y","typeReferences":[["Subtype"],["SetLike","instMembership"],["Module"],["instHAdd"],["Membership","mem"],["Subtype","val"],["Submodule"],["HAdd","hAdd"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Submodule","setLike"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Submodule","addCommMonoid"],["Eq"],["Semiring"]],"valueReferences":[["Subtype"],["SetLike","instMembership"],["True"],["Eq","trans"],["instHAdd"],["Membership","mem"],["Subtype","val"],["Submodule"],["HAdd","hAdd"],["implies_true"],["eq_self"],["of_eq_true"],["AddCommMonoid","toAddCommSemigroup"],["Submodule","setLike"],["forall_congr"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","domRestrict'","_proof_1"],"typeFallback":"forall {R : Type.{u_1}} {M₂ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11 : CommSemiring.{u_1} R] 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Type.{u_7}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.11 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.14 : Semiring.{u_3} R₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.26 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.40 : Module.{u_3, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.26] {σ₁₂ : RingHom.{u_1, u_3} R R₂ 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.40 σ₁₂) f c)} (x : M), Eq.{succ u_7} M₂ (Subtype.val.{succ u_7} M₂ (fun (x : M₂) => Membership.mem.{u_7, u_7} M₂ (Submodule.{u_3, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.40) (SetLike.instMembership.{u_7, u_7} (Submodule.{u_3, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_3, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3007290468._hygCtx._hyg.14 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(x : M), ↑((LinearMap.codRestrict p f h) x) = f x","typeReadable":"∀ {R : Type u_1} {R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n (p : Submodule R₂ M₂) (f : M →ₛₗ[σ₁₂] M₂) {h : ∀ (c : M), f c ∈ p} (x : M), ↑((LinearMap.codRestrict p f h) x) = f 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{module_M : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10} (p : Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (m : R) (x : Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)), Eq.{succ u_1} M (Subtype.val.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x) (HSMul.hSMul.{u_2, u_1, u_1} R (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (instHSMul.{u_2, u_1} R (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (SMulZeroClass.toSMul.{u_2, u_1} R (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (AddZero.toZero.{u_1} (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (AddZeroClass.toAddZero.{u_1} (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (AddMonoid.toAddZeroClass.{u_1} (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (AddCommMonoid.toAddMonoid.{u_1} (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (Submodule.addCommMonoid.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M p))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (AddMonoid.toAddZeroClass.{u_1} (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (AddCommMonoid.toAddMonoid.{u_1} (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M)) p x)) (Submodule.addCommMonoid.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M p))) (DistribMulAction.toDistribSMul.{u_2, u_1} R (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M 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[inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 : AddCommMonoid.{u_11} M₃] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 : Module.{u_1, u_10} R M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92 : Module.{u_1, u_11} R M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85] {p : Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32} {p₂ : Submodule.{u_1, u_10} R M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88} {p₃ : Submodule.{u_1, u_11} R M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92} {f : LinearMap.{u_1, u_1, u_5, u_10} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88} {g : LinearMap.{u_1, u_1, u_10, u_11} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) M₂ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92} (hf : Set.MapsTo.{u_5, u_10} M M₂ (DFunLike.coe.{max (succ u_10) (succ u_5), succ u_5, succ u_10} (LinearMap.{u_1, u_1, u_5, u_10} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_5, u_10} R R M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11))) f) (SetLike.coe.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32) p) (SetLike.coe.{u_10, u_10} (Submodule.{u_1, u_10} R M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88) M₂ (Submodule.setLike.{u_1, u_10} R M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88) p₂)) (hg : Set.MapsTo.{u_10, u_11} M₂ M₃ (DFunLike.coe.{max (succ u_10) (succ u_11), succ u_10, succ u_11} (LinearMap.{u_1, u_1, u_10, u_11} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) M₂ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92) M₂ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂) => M₃) (LinearMap.instFunLike.{u_1, u_1, u_10, u_11} R R M₂ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11))) g) (SetLike.coe.{u_10, u_10} 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92) p₃)) (hfg : optParam.{0} (Set.MapsTo.{u_5, u_11} M M₃ (DFunLike.coe.{max (succ u_11) (succ u_5), succ u_5, succ u_11} (LinearMap.{u_1, u_1, u_5, u_11} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) M M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₃) (LinearMap.instFunLike.{u_1, u_1, u_5, u_11} R R M M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11))) (LinearMap.comp.{u_1, u_1, u_1, u_5, u_10, u_11} R R R M M₂ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11))) g f)) (SetLike.coe.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32) p) (SetLike.coe.{u_11, u_11} (Submodule.{u_1, u_11} R M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92) M₃ (Submodule.setLike.{u_1, u_11} R M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92) p₃)) (Set.MapsTo.comp.{u_5, u_10, u_11} M M₂ M₃ (SetLike.coe.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32) p) (SetLike.coe.{u_10, u_10} (Submodule.{u_1, u_10} R M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88) M₂ (Submodule.setLike.{u_1, u_10} R M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88) p₂) (SetLike.coe.{u_11, u_11} (Submodule.{u_1, u_11} R M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92) M₃ (Submodule.setLike.{u_1, u_11} R M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92) p₃) (DFunLike.coe.{max (succ u_10) (succ u_5), succ u_5, succ u_10} (LinearMap.{u_1, u_1, u_5, u_10} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_1, u_1, u_5, u_10} R R M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11))) f) (DFunLike.coe.{max (succ u_10) (succ u_11), succ u_10, succ u_11} (LinearMap.{u_1, u_1, u_10, u_11} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) M₂ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92) M₂ (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂) => M₃) (LinearMap.instFunLike.{u_1, u_1, u_10, u_11} R R M₂ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.82 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.92 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.699777177._hygCtx._hyg.11)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10)) p x)) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10)) p x)) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.10)) p x)) M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4225300190._hygCtx._hyg.4 (Submodule.addCommMonoid.{u_2, u_1} R M 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[inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20] {f : LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32} {g : LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32}, (Commute.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) (Module.End.instMul.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) f g) -> (forall {p : Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32} (hf : Set.MapsTo.{u_5, u_5} M M (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11))) f) (SetLike.coe.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) p) (SetLike.coe.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) p)) (hg : Set.MapsTo.{u_5, u_5} M M (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11))) g) (SetLike.coe.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) p) (SetLike.coe.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) p)), Commute.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32)) p x)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32)) p x)) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 p) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 p)) (Module.End.instMul.{u_1, u_5} R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32)) p x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 p)) (LinearMap.restrict.{u_1, u_5, u_5} R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.32 f p p hf) (LinearMap.restrict.{u_1, u_5, u_5} R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3893330998._hygCtx._hyg.11 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{R : Type.{u}} {M : Type.{v}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 : Semiring.{u} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 : AddCommMonoid.{v} M] {module_M : Module.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10} (p : Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.10 module_M), LinearMap.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971593._hygCtx._hyg.7)) (Subtype.{succ v} M (fun (x : M) => Membership.mem.{v, v} M (Submodule.{u, v} R M 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.10)) p x)) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.10) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.10) M (Submodule.setLike.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.7 (Submodule.module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.10 p) (Submodule.module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.10 q) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.10 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4)) (RingHom.id.{u_1} R 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(Submodule.subtype.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.289814044._hygCtx._hyg.10 p)","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n (p q : Submodule R M) (h : p ≤ q), q.subtype ∘ₗ Submodule.inclusion h = p.subtype","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]\n (p q : Submodule R M) (h : p ≤ q), q.subtype ∘ₗ Submodule.inclusion h = p.subtype","typeReferences":[["SetLike","instMembership"],["PartialOrder","toPreorder"],["Subtype"],["RingHomCompTriple","ids"],["Module"],["Submodule","module"],["Membership","mem"],["Submodule","instPartialOrder"],["LinearMap","comp"],["LinearMap"],["Submodule","subtype"],["Submodule"],["Submodule","inclusion"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["Submodule","setLike"],["RingHom","id"],["LE","le"],["Submodule","addCommMonoid"],["Preorder","toLE"],["Eq"],["Semiring"]],"valueReferences":[["rfl"],["Subtype"],["SetLike","instMembership"],["RingHomCompTriple","ids"],["Submodule","module"],["Membership","mem"],["LinearMap","comp"],["LinearMap"],["Submodule","subtype"],["Submodule"],["Submodule","inclusion"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Submodule","setLike"],["Submodule","addCommMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","restrict_sub"],"typeFallback":"forall {R : Type.{u_10}} {M : Type.{u_11}} {M₁ : Type.{u_12}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83 : Ring.{u_10} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86 : AddCommGroup.{u_11} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89 : AddCommGroup.{u_12} M₁] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 : Module.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86)] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 : Module.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89)] {p : Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92} {q : Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96} {f : LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96} {g : LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96} (hf : Set.MapsTo.{u_11, u_12} M M₁ (DFunLike.coe.{max (succ u_11) (succ u_12), succ u_11, succ u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₁) (LinearMap.instFunLike.{u_10, u_10, u_11, u_12} R R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83)))) f) (SetLike.coe.{u_11, u_11} (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) p) (SetLike.coe.{u_12, u_12} (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) q)) (hg : Set.MapsTo.{u_11, u_12} M M₁ (DFunLike.coe.{max (succ u_11) (succ u_12), succ u_11, succ u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₁) (LinearMap.instFunLike.{u_10, u_10, u_11, u_12} R R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83)))) g) (SetLike.coe.{u_11, u_11} (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) p) (SetLike.coe.{u_12, u_12} (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) q)) (hfg : 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M₁) (LinearMap.instFunLike.{u_10, u_10, u_11, u_12} R R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83)))) (HSub.hSub.{max u_11 u_12, max u_11 u_12, max u_11 u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (instHSub.{max u_11 u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (LinearMap.instSub.{u_10, u_10, u_11, u_12} R R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))))) f g)) (SetLike.coe.{u_11, u_11} (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) p) (SetLike.coe.{u_12, u_12} (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) q)) (fun (x._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.148 : M) (hx : Membership.mem.{u_11, u_11} M (Set.{u_11} M) (Set.instMembership.{u_11} M) (SetLike.coe.{u_11, u_11} (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) p) x._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.148) => Submodule.sub_mem.{u_10, u_12} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q (DFunLike.coe.{max (succ u_12) (succ u_11), succ u_11, succ u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₁) (LinearMap.instFunLike.{u_10, u_10, u_11, u_12} R R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83)))) f x._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.148) (DFunLike.coe.{max (succ u_12) (succ u_11), succ u_11, succ u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₁) (LinearMap.instFunLike.{u_10, u_10, u_11, u_12} R R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) 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(AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96)) q x)) (Submodule.addCommMonoid.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.addCommMonoid.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q) (Submodule.module.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.module.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q)) (HSub.hSub.{max u_11 u_12, max u_11 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92)) p x)) (Subtype.{succ u_12} M₁ (fun (x : M₁) => Membership.mem.{u_12, u_12} M₁ (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (SetLike.instMembership.{u_12, u_12} (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96)) q x)) (Submodule.addCommMonoid.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.addCommMonoid.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q) (Submodule.module.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.module.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q)) (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92)) p x)) (Subtype.{succ u_12} M₁ (fun (x : M₁) => Membership.mem.{u_12, u_12} M₁ (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (SetLike.instMembership.{u_12, u_12} (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96)) q x)) (Submodule.addCommMonoid.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.addCommMonoid.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q) (Submodule.module.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.module.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q)) (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92)) p x)) (Subtype.{succ u_12} M₁ (fun (x : M₁) => Membership.mem.{u_12, u_12} M₁ (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (SetLike.instMembership.{u_12, u_12} (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96)) q x)) (Submodule.addCommMonoid.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.addCommMonoid.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q) (Submodule.module.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.module.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q)) (instHSub.{max u_11 u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92)) p x)) (Subtype.{succ u_12} M₁ (fun (x : M₁) => Membership.mem.{u_12, u_12} M₁ (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (SetLike.instMembership.{u_12, u_12} (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96)) q x)) (Submodule.addCommMonoid.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.addCommMonoid.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q) (Submodule.module.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.module.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q)) (LinearMap.instSub.{u_10, u_10, u_11, u_12} R R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92) M (Submodule.setLike.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92)) p x)) (Subtype.{succ u_12} M₁ (fun (x : M₁) => Membership.mem.{u_12, u_12} M₁ (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (SetLike.instMembership.{u_12, u_12} (Submodule.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) M₁ (Submodule.setLike.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96)) q x)) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Submodule.addCommMonoid.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.addCommGroup.{u_10, u_12} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q) (Submodule.module.{u_10, u_11} R M (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 p) (Submodule.module.{u_10, u_12} R M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 q) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))))) (LinearMap.restrict.{u_10, u_11, u_12} R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 f p q hf) (LinearMap.restrict.{u_10, u_11, u_12} R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 g p q hg)) (LinearMap.restrict.{u_10, u_11, u_12} R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 (HSub.hSub.{max u_11 u_12, max u_11 u_12, max u_11 u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (instHSub.{max u_11 u_12} (LinearMap.{u_10, u_10, u_11, u_12} R R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))) M M₁ (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) (AddCommGroup.toAddCommMonoid.{u_12} M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96) (LinearMap.instSub.{u_10, u_10, u_11, u_12} R R M M₁ (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83) (AddCommGroup.toAddCommMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.86) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.89 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.92 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.96 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (Ring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.4196434567._hygCtx._hyg.83))))) f g) p q hfg)","typeFull":"∀ {R : Type u_10} {M : Type u_11} {M₁ : Type u_12} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup M₁]\n [inst_3 : Module R M] [inst_4 : Module R M₁] {p : Submodule R M} {q : Submodule R M₁} {f g : M →ₗ[R] M₁}\n (hf : Set.MapsTo ⇑f ↑p ↑q) (hg : Set.MapsTo ⇑g ↑p ↑q) (hfg : optParam (Set.MapsTo ⇑(f - g) ↑p ↑q) ⋯),\n f.restrict hf - g.restrict hg = (f - g).restrict hfg","typeReadable":"∀ {R : Type u_10} {M : Type u_11} {M₁ : Type u_12} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup M₁]\n [inst_3 : Module R M] [inst_4 : Module R M₁] {p : Submodule R M} {q : Submodule R M₁} {f g : M →ₗ[R] M₁}\n (hf : Set.MapsTo ⇑f ↑p ↑q) (hg : Set.MapsTo ⇑g ↑p ↑q) (hfg : optParam (Set.MapsTo ⇑(f - g) ↑p ↑q) ⋯),\n f.restrict hf - g.restrict hg = (f - g).restrict hfg","typeReferences":[["Subtype"],["LinearMap","instFunLike"],["Module"],["Submodule","module"],["Membership","mem"],["DFunLike","coe"],["Submodule"],["Semiring","toNonAssocSemiring"],["LinearMap","restrict"],["RingHom","id"],["HSub","hSub"],["Eq"],["SetLike","instMembership"],["Submodule","addCommGroup"],["AddCommGroup"],["LinearMap"],["Ring","toSemiring"],["Set","MapsTo"],["SetLike","coe"],["Submodule","setLike"],["optParam"],["LinearMap","instSub"],["AddCommGroup","toAddCommMonoid"],["Submodule","sub_mem"],["instHSub"],["Submodule","addCommMonoid"],["Ring"]],"valueReferences":[["Subtype"],["LinearMap","instFunLike"],["AddCommGroup","toAddGroup"],["Submodule","module"],["Membership","mem"],["Subtype","val"],["DFunLike","coe"],["Submodule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["LinearMap","restrict"],["LinearMap","ext"],["SubNegMonoid","toSub"],["HSub","hSub"],["AddGroup","toSubNegMonoid"],["Eq"],["SetLike","instMembership"],["Submodule","addCommGroup"],["Subtype","ext"],["LinearMap"],["Ring","toSemiring"],["eq_self"],["of_eq_true"],["Submodule","setLike"],["LinearMap","instSub"],["AddCommGroup","toAddCommMonoid"],["Submodule","addCommMonoid"],["instHSub"]]},{"isProp":true,"kind":"theorem","name":["Submodule","inclusion_injective"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10 : Module.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7] {p : Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10} {p' : Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10} (h : LE.le.{u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) (Preorder.toLE.{u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) (PartialOrder.toPreorder.{u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) (Submodule.instPartialOrder.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10))) p p'), Function.Injective.{succ u_2, succ u_2} (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) M (Submodule.setLike.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10)) p x)) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) M (Submodule.setLike.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10)) p' x)) (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearMap.{u_1, u_1, u_2, u_2} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4)) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) M (Submodule.setLike.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10)) p x)) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.10) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3858940581._hygCtx._hyg.7 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81] (p : LinearMap.{u_3, u_3, u_1, u_2} R₂ R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 (RingHom.id.{u_3} R₂ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14)) M₂' M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.84 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40), (Function.Injective.{succ u_1, succ u_2} M₂' M₂ (DFunLike.coe.{max (succ u_1) (succ u_2), succ u_1, succ u_2} (LinearMap.{u_3, u_3, u_1, u_2} R₂ R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 (RingHom.id.{u_3} R₂ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14)) M₂' M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.84 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40) M₂' (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂') => M₂) (LinearMap.instFunLike.{u_3, u_3, u_1, u_2} R₂ R₂ M₂' M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_5, u_3, u_4, u_2} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40 σ₁₂) f c)) (h c))))","typeFull":"∀ {R : Type u_5} {R₂ : Type u_3} {M : Type u_4} {M₂ : Type u_2} [inst : Semiring R] [inst_1 : Semiring R₂]\n [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n (f : M →ₛₗ[σ₁₂] M₂) {M₂' : Type u_1} [inst_6 : AddCommMonoid M₂'] [inst_7 : Module R₂ M₂'] (p : M₂' →ₗ[R₂] M₂),\n Function.Injective ⇑p →\n ∀ (h : ∀ (c : M), f c ∈ Set.range ⇑p) (r : R) (c : M), Exists.choose ⋯ = σ₁₂ r • Exists.choose ⋯","typeReadable":"∀ {R : Type u_5} {R₂ : Type u_3} {M : Type u_4} {M₂ : Type u_2} [inst : Semiring R] [inst_1 : Semiring R₂]\n [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n (f : M →ₛₗ[σ₁₂] M₂) {M₂' : Type u_1} [inst_6 : AddCommMonoid M₂'] [inst_7 : Module R₂ M₂'] (p : M₂' →ₗ[R₂] M₂),\n Function.Injective ⇑p →\n ∀ (h : ∀ (c : M), f c ∈ Set.range ⇑p) (r : R) (c : M), Exists.choose ⋯ = σ₁₂ r • Exists.choose ⋯","typeReferences":[["RingHom"],["LinearMap","instFunLike"],["Module"],["Membership","mem"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Set","range"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["DistribSMul","toSMulZeroClass"],["Set"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearMap"],["Exists","choose"],["AddZeroClass","toAddZero"],["Set","instMembership"],["Module","toDistribMulAction"],["HSMul","hSMul"],["AddZero","toZero"],["Function","Injective"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["RingHom"],["Eq","trans"],["LinearMap","instFunLike"],["RingHom","instFunLike"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["map_smul"],["congrArg"],["LinearMap","semilinearMapClass"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["congr"],["MonoidWithZero","toMonoid"],["instHSMul"],["congrFun'"],["Eq"],["DistribSMul","toSMulZeroClass"],["SemilinearMapClass","toMulActionSemiHomClass"],["True"],["Exists","choose_spec"],["outParam"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["Exists","choose"],["eq_self"],["MulActionSemiHomClass","map_smulₛₗ"],["Module","toDistribMulAction"],["of_eq_true"],["HSMul","hSMul"],["id"],["Eq","mpr"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["SMulMemClass","subtype","_proof_2"],"typeFallback":"forall {R : Type.{u_3}} {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.7 : Semiring.{u_3} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.10 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.13 : Module.{u_3, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.10] {A : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.18 : SetLike.{u_2, u_1} A M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.22 : AddSubmonoidClass.{u_2, u_1} A M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1027971592._hygCtx._hyg.18] 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11)) M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₁) (LinearMap.instFunLike.{u_2, u_2, u_1, u_3} R R M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32)) p x)), Membership.mem.{u_3, u_3} M₁ (Submodule.{u_2, u_3} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) (SetLike.instMembership.{u_3, u_3} (Submodule.{u_2, u_3} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) M₁ (Submodule.setLike.{u_2, u_3} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36)) q (DFunLike.coe.{max (succ u_1) (succ u_3), succ u_1, succ u_3} (LinearMap.{u_2, u_2, u_1, u_3} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11)) (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) (SetLike.instMembership.{u_1, u_1} 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32)) p x)) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) M (Submodule.setLike.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32)) p x)) => M₁) (LinearMap.instFunLike.{u_2, u_2, u_1, u_3} R R (Subtype.{succ u_1} M (fun (x : M) => Membership.mem.{u_1, u_1} M (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) M (Submodule.setLike.{u_2, u_1} R M 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Type u_1} {M₁ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] (f : M →ₗ[R] M₁) {p : Submodule R M}\n {q : Submodule R M₁}, (∀ x ∈ p, f x ∈ q) → ∀ (x : ↥p), (f.domRestrict p) x ∈ q","typeReadable":"∀ {R : Type u_2} {M : Type u_1} {M₁ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M]\n [inst_2 : AddCommMonoid M₁] [inst_3 : Module R M] [inst_4 : Module R M₁] (f : M →ₗ[R] M₁) {p : Submodule R M}\n {q : Submodule R M₁}, (∀ x ∈ p, f x ∈ q) → ∀ (x : ↥p), (f.domRestrict p) x ∈ 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[inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.23 : AddCommMonoid.{u_6} M₁] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.36 : Module.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.23] {f : LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_6, u_6} M₁ (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.36) (SetLike.instMembership.{u_6, u_6} (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.36) M₁ (Submodule.setLike.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.36)) q (DFunLike.coe.{max (succ u_5) (succ u_6), succ u_5, succ u_6} (LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11)) M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.36) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₁) (LinearMap.instFunLike.{u_1, u_1, u_5, u_6} R R M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3704370039._hygCtx._hyg.32 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(Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.domRestrict.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (HAdd.hAdd.{max u_2 u_3, max u_2 u_3, max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (instHAdd.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommMagma.toAdd.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommSemigroup.toAddCommMagma.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommMonoid.toAddCommSemigroup.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))))))) x y) p) (HAdd.hAdd.{max u_2 u_3, max u_2 u_3, max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (instHAdd.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommMagma.toAdd.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommSemigroup.toAddCommMagma.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (AddCommMonoid.toAddCommSemigroup.{max u_2 u_3} (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R (Subtype.{succ u_2} M (fun (x : M) => Membership.mem.{u_2, u_2} M (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) (SetLike.instMembership.{u_2, u_2} (Submodule.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 (Submodule.module.{u_1, u_2} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11)))))))) (LinearMap.domRestrict.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) x p) (LinearMap.domRestrict.{u_1, u_1, u_2, u_3} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.511706315._hygCtx._hyg.11))) y p))","typeFull":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (p : Submodule R M) (x y : M →ₗ[R] M₂),\n (x + y).domRestrict p = x.domRestrict p + y.domRestrict p","typeReadable":"∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]\n [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (p : Submodule R M) (x y : M →ₗ[R] M₂),\n (x + y).domRestrict p = x.domRestrict p + y.domRestrict 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{R : Type.{u_10}} {M : Type.{u_11}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82 : CommSemiring.{u_10} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 : AddCommMonoid.{u_11} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 : Module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85] {p : Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88} (μ : R) (h : optParam.{0} (forall (x : M), (Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x) -> (Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p (DFunLike.coe.{succ u_11, succ u_11, succ u_11} (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_10, u_10, u_11, u_11} R R M M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82)))) (HSMul.hSMul.{u_10, u_11, u_11} R (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (instHSMul.{u_10, u_11} R (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (LinearMap.instSMul.{u_10, u_10, u_10, u_11, u_11} R R R M M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82))) (DistribMulAction.toDistribSMul.{u_10, u_11} R M (MonoidWithZero.toMonoid.{u_10} R (Semiring.toMonoidWithZero.{u_10} R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82))) (AddCommMonoid.toAddMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85) (Module.toDistribMulAction.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) (smulCommClass_self.{u_10, u_11} R M (CommSemiring.toCommMonoid.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (DistribMulAction.toMulAction.{u_10, u_11} R M (CommMonoid.toMonoid.{u_10} R (CommSemiring.toCommMonoid.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82)) (AddCommMonoid.toAddMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85) (Module.toDistribMulAction.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88))))) μ (OfNat.ofNat.{u_11} (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) 1 (One.toOfNat1.{u_11} (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (Module.End.instOne.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)))) x))) (fun (x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.137 : M) => Submodule.smul_mem.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.137 μ)), Eq.{succ u_11} (LinearMap.{u_10, u_10, u_11, u_11} R R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82))) (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p)) (LinearMap.restrict.{u_10, u_11, u_11} R M M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 (HSMul.hSMul.{u_10, u_11, u_11} R (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (instHSMul.{u_10, u_11} R (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (LinearMap.instSMul.{u_10, u_10, u_10, u_11, u_11} R R R M M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82))) (DistribMulAction.toDistribSMul.{u_10, u_11} R M (MonoidWithZero.toMonoid.{u_10} R (Semiring.toMonoidWithZero.{u_10} R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82))) (AddCommMonoid.toAddMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85) (Module.toDistribMulAction.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) (smulCommClass_self.{u_10, u_11} R M (CommSemiring.toCommMonoid.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (DistribMulAction.toMulAction.{u_10, u_11} R M (CommMonoid.toMonoid.{u_10} R (CommSemiring.toCommMonoid.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82)) (AddCommMonoid.toAddMonoid.{u_11} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85) (Module.toDistribMulAction.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88))))) μ (OfNat.ofNat.{u_11} (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) 1 (One.toOfNat1.{u_11} (Module.End.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (Module.End.instOne.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)))) p p h) (HSMul.hSMul.{u_10, u_11, u_11} R (Module.End.{u_10, u_11} R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p)) (Module.End.{u_10, u_11} R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p)) (instHSMul.{u_10, u_11} R (Module.End.{u_10, u_11} R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p)) (LinearMap.instSMul.{u_10, u_10, u_10, u_11, u_11} R R R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (RingHom.id.{u_10} R (Semiring.toNonAssocSemiring.{u_10} R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82))) (DistribMulAction.toDistribSMul.{u_10, u_11} R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (MonoidWithZero.toMonoid.{u_10} R (Semiring.toMonoidWithZero.{u_10} R (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82))) (AddCommMonoid.toAddMonoid.{u_11} (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p)) (Module.toDistribMulAction.{u_10, u_11} R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p))) (smulCommClass_self.{u_10, u_11} R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (CommSemiring.toCommMonoid.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (DistribMulAction.toMulAction.{u_10, u_11} R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (CommMonoid.toMonoid.{u_10} R (CommSemiring.toCommMonoid.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82)) (AddCommMonoid.toAddMonoid.{u_11} (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p)) (Module.toDistribMulAction.{u_10, u_11} R (Subtype.{succ u_11} M (fun (x : M) => Membership.mem.{u_11, u_11} M (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) (SetLike.instMembership.{u_11, u_11} (Submodule.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88) M (Submodule.setLike.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88)) p x)) (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) (Submodule.addCommMonoid.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.82) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.85 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2298323851._hygCtx._hyg.88 p) (Submodule.module.{u_10, u_11} R M (CommSemiring.toSemiring.{u_10} R 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[inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 : Semiring.{u_3} R₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40 : Module.{u_3, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26] {σ₁₂ : RingHom.{u_1, u_3} R R₂ (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.11) 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81] (p : LinearMap.{u_3, u_3, u_10, u_7} R₂ R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 (RingHom.id.{u_3} R₂ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14)) M₂' M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.84 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40), (Function.Injective.{succ u_10, succ u_7} M₂' M₂ (DFunLike.coe.{max (succ u_10) (succ u_7), succ u_10, succ u_7} (LinearMap.{u_3, u_3, u_10, u_7} R₂ R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 (RingHom.id.{u_3} R₂ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14)) M₂' M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.84 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40) M₂' (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂') => M₂) (LinearMap.instFunLike.{u_3, u_3, u_10, u_7} R₂ R₂ M₂' M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.84 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40 (RingHom.id.{u_3} R₂ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14))) p)) -> (forall (c : M), Membership.mem.{u_7, u_7} M₂ (Set.{u_7} M₂) (Set.instMembership.{u_7} M₂) (Set.range.{u_7, succ u_10} M₂ M₂' (DFunLike.coe.{max (succ u_10) (succ u_7), succ u_10, succ u_7} (LinearMap.{u_3, u_3, u_10, u_7} R₂ R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 (RingHom.id.{u_3} R₂ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14)) M₂' M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 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Type u_10} →\n [inst_6 : AddCommMonoid M₂'] →\n [inst_7 : Module R₂ M₂'] →\n (p : M₂' →ₗ[R₂] M₂) →\n Function.Injective ⇑p → (∀ (c : M), f c ∈ Set.range ⇑p) → M →ₛₗ[σ₁₂] M₂'","typeReadable":"{R : Type u_1} →\n {R₂ : Type u_3} →\n {M : Type u_5} →\n {M₂ : Type u_7} →\n [inst : Semiring R] →\n [inst_1 : Semiring R₂] →\n [inst_2 : AddCommMonoid M] →\n [inst_3 : AddCommMonoid M₂] →\n [inst_4 : Module R M] →\n [inst_5 : Module R₂ M₂] →\n {σ₁₂ : R →+* R₂} →\n (f : M →ₛₗ[σ₁₂] M₂) →\n {M₂' : Type u_10} →\n [inst_6 : AddCommMonoid M₂'] →\n [inst_7 : Module R₂ M₂'] →\n (p : M₂' →ₗ[R₂] M₂) →\n Function.Injective ⇑p → (∀ (c : M), f c ∈ Set.range ⇑p) → M →ₛₗ[σ₁₂] M₂'","typeReferences":[["RingHom"],["LinearMap","instFunLike"],["Module"],["Set"],["Membership","mem"],["LinearMap"],["DFunLike","coe"],["Set","range"],["Set","instMembership"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Semiring"],["Function","Injective"]],"valueReferences":[["LinearMap","codLift","_proof_2"],["LinearMap","instFunLike"],["LinearMap","codLift","_proof_3"],["LinearMap","mk"],["AddHom","mk"],["Exists","choose"],["LinearMap"],["DFunLike","coe"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","restrict_coe_apply"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} {M₁ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.11 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.20 : AddCommMonoid.{u_5} 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.36) {p : Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.32} {q : Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.36} (hf : forall (x : M), (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_6, u_6} M₁ (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.3055065877._hygCtx._hyg.23 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11))) f' x))) (h' : optParam.{0} (forall (x : M), (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p (DFunLike.coe.{succ u_5, succ u_5, succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M) (LinearMap.instFunLike.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11))) (HPow.hPow.{u_5, 0, u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) Nat (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (instHPow.{u_5, 0} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) Nat (Monoid.toPow.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (Module.End.instMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32))) f' n) x))) (Module.End.pow_apply_mem_of_forall_mem.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 f' p n h)), Eq.{succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p)) (HPow.hPow.{u_5, 0, u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p)) Nat (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p)) (instHPow.{u_5, 0} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p)) Nat (Monoid.toPow.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p)) (Module.End.instMonoid.{u_1, u_5} R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32)) p x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 p)))) (LinearMap.restrict.{u_1, u_5, u_5} R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 f' p p h) n) (LinearMap.restrict.{u_1, u_5, u_5} R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 (HPow.hPow.{u_5, 0, u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) Nat (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (instHPow.{u_5, 0} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) Nat (Monoid.toPow.{u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32) (Module.End.instMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1146606405._hygCtx._hyg.32))) f' n) p p h')","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {f' : M →ₗ[R] M}\n {p : Submodule R M} (n : ℕ) (h : ∀ x ∈ p, f' x ∈ p) (h' : optParam (∀ x ∈ p, (f' ^ n) x ∈ p) ⋯),\n f'.restrict h ^ n = (f' ^ n).restrict h'","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {f' : M →ₗ[R] M}\n {p : Submodule R M} (n : ℕ) (h : ∀ x ∈ p, f' x ∈ p) (h' : optParam (∀ x ∈ p, (f' ^ n) x ∈ p) ⋯),\n f'.restrict h ^ n = (f' ^ n).restrict h'","typeReferences":[["instHPow"],["Subtype"],["SetLike","instMembership"],["LinearMap","instFunLike"],["Module"],["Submodule","module"],["Membership","mem"],["HPow","hPow"],["LinearMap"],["DFunLike","coe"],["Submodule"],["AddCommMonoid"],["Nat"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["LinearMap","restrict"],["optParam"],["RingHom","id"],["Submodule","setLike"],["Module","End","instMonoid"],["Submodule","addCommMonoid"],["Eq"],["Module","End","pow_apply_mem_of_forall_mem"],["Semiring"]],"valueReferences":[["Subtype"],["LinearMap","instFunLike"],["Eq","trans"],["Submodule","module"],["Membership","mem"],["DFunLike","coe"],["Subtype","val"],["congrArg"],["Submodule"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["congrFun"],["RingHom","id"],["LinearMap","restrict"],["congr"],["LinearMap","ext"],["Eq"],["Module","End","coe_pow"],["instHPow"],["Function","Semiconj","iterate_right"],["Module","End"],["SetLike","instMembership"],["True"],["Subtype","ext"],["LinearMap"],["HPow","hPow"],["LinearMap","restrict_coe_apply"],["eq_self"],["Nat"],["Nat","iterate"],["of_eq_true"],["Submodule","setLike"],["Module","End","instMonoid"],["Submodule","addCommMonoid"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","restrict","congr_simp"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_5}} {M₁ : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 : AddCommMonoid.{u_6} M₁] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36 : Module.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23] (f : LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11)) M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) (f_1 : LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11)) M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) (e_f : Eq.{max (succ u_5) (succ u_6)} (LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11)) M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) f f_1) {p : Submodule.{u_1, u_5} R M 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_6, u_6} M₁ (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) (SetLike.instMembership.{u_6, u_6} (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) M₁ (Submodule.setLike.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36)) q (DFunLike.coe.{max (succ u_5) (succ u_6), succ u_5, succ u_6} (LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11)) M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₁) (LinearMap.instFunLike.{u_1, u_1, u_5, u_6} R R M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11))) f x))), Eq.{max (succ u_5) (succ u_6)} (LinearMap.{u_1, u_1, u_5, u_6} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_6, u_6} M₁ (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) (SetLike.instMembership.{u_6, u_6} (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 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[inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.11 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.14 : Semiring.{u_3} R₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.20 : AddCommMonoid.{u_5} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.26 : AddCommMonoid.{u_7} M₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.32 : Module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.40 : Module.{u_3, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2406454333._hygCtx._hyg.26] {σ₁₂ : RingHom.{u_1, u_3} R R₂ (Semiring.toNonAssocSemiring.{u_1} R 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{R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n (f : M →ₛₗ[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ (b : M), f b ∈ p), p.subtype ∘ₛₗ LinearMap.codRestrict p f h = f","typeReadable":"∀ {R : Type u_1} {R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]\n [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}\n (f : M →ₛₗ[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ (b : M), f b ∈ p), p.subtype ∘ₛₗ LinearMap.codRestrict p f h = 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (smulCommClass_self.{u_1, u_7} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (DistribMulAction.toMulAction.{u_1, u_7} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17) (Module.toDistribMulAction.{u_1, u_7} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_7} R R R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 (Submodule.module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (smulCommClass_self.{u_1, u_7} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (DistribMulAction.toMulAction.{u_1, u_7} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17) (Module.toDistribMulAction.{u_1, u_7} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24))))) (LinearMap.{u_1, u_1, u_5, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_5, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24) => LinearMap.{u_1, u_1, u_5, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11))) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 (Submodule.module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24) (LinearMap.instFunLike.{u_1, u_1, max u_5 u_7, max u_5 u_7} R R (LinearMap.{u_1, u_1, u_5, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11))) M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24) (LinearMap.{u_1, u_1, u_5, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11))) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20)) p x)) M₂ (Submodule.addCommMonoid.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 (Submodule.module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_7} R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11)))) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_7} R R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 (Submodule.module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_7} R R R M M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (smulCommClass_self.{u_1, u_7} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (DistribMulAction.toMulAction.{u_1, u_7} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11)) (AddCommMonoid.toAddMonoid.{u_7} M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17) (Module.toDistribMulAction.{u_1, u_7} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_7} R R R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20) M (Submodule.setLike.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20)) p x)) M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) (Submodule.addCommMonoid.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.17 (Submodule.module.{u_1, u_5} R M (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.11) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.20 p) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1181051300._hygCtx._hyg.24 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R 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AddCommMonoid.{u_2} M₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.32 : Module.{u_5, u_4} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40 : Module.{u_3, u_2} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26] {σ₁₂ : RingHom.{u_5, u_3} R R₂ (Semiring.toNonAssocSemiring.{u_5} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.11) (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14)} (f : LinearMap.{u_5, u_3, u_4, u_2} R R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40) {M₂' : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 : AddCommMonoid.{u_1} M₂'] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.84 : Module.{u_3, u_1} R₂ M₂' inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81] (p : LinearMap.{u_3, u_3, u_1, u_2} R₂ R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.84 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40) M₂' (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₂') => M₂) (LinearMap.instFunLike.{u_3, u_3, u_1, u_2} R₂ R₂ M₂' M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.81 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.84 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.40 (RingHom.id.{u_3} R₂ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2737938913._hygCtx._hyg.14))) p)) -> (forall (h 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11)) M M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) {p : Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32} {q : Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36}, (forall (x : M), (Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32)) p x) -> (Membership.mem.{u_6, u_6} M₁ (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) (SetLike.instMembership.{u_6, u_6} (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) M₁ (Submodule.setLike.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36)) q (DFunLike.coe.{max (succ u_5) (succ u_6), succ u_5, succ u_6} (LinearMap.{u_1, u_1, u_5, u_6} R R 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.32)) p x)) (Subtype.{succ u_6} M₁ (fun (x : M₁) => Membership.mem.{u_6, u_6} M₁ (Submodule.{u_1, u_6} R M₁ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.23 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1719140914._hygCtx._hyg.36) 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N)} {G : Module.End.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32}, (Eq.{succ u_5} (LinearMap.{u_1, u_1, u_5, u_5} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)) (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) M (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (LinearMap.comp.{u_1, u_1, u_1, u_5, u_5, u_5} R R R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)) 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)) (RingHomCompTriple.ids.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11))) (Submodule.subtype.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) g)) -> (forall {k : Nat}, (Eq.{succ u_5} (Module.End.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (HPow.hPow.{u_5, 0, u_5} (Module.End.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) Nat (Module.End.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (instHPow.{u_5, 0} (Module.End.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) Nat (Monoid.toPow.{u_5} (Module.End.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (Module.End.instMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32))) G k) (OfNat.ofNat.{u_5} (Module.End.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) 0 (Zero.toOfNat0.{u_5} (Module.End.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (LinearMap.instZero.{u_1, u_1, u_5, u_5} R R M M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)))))) -> (Eq.{succ u_5} (Module.End.{u_1, u_5} R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N)) (HPow.hPow.{u_5, 0, u_5} (Module.End.{u_1, u_5} R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N)) Nat (Module.End.{u_1, u_5} R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N)) (instHPow.{u_5, 0} (Module.End.{u_1, u_5} R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N)) Nat (Monoid.toPow.{u_5} (Module.End.{u_1, u_5} R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N) (Submodule.module.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32 N)) (LinearMap.instZero.{u_1, u_1, u_5, u_5} R R (Subtype.{succ u_5} M (fun (x : M) => Membership.mem.{u_5, u_5} M (Submodule.{u_1, u_5} R M 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) (SetLike.instMembership.{u_5, u_5} (Submodule.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32) M (Submodule.setLike.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.32)) N x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 (Submodule.addCommMonoid.{u_1, u_5} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11 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(Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.605554926._hygCtx._hyg.11)))))))","typeFull":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N : Submodule R M}\n {g : Module.End R ↥N} {G : Module.End R M}, G ∘ₗ N.subtype = N.subtype ∘ₗ g → ∀ {k : ℕ}, G ^ k = 0 → g ^ k = 0","typeReadable":"∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N : Submodule R M}\n {g : Module.End R ↥N} {G : Module.End R M}, G ∘ₗ N.subtype = N.subtype ∘ₗ g → ∀ {k : ℕ}, G ^ k = 0 → g ^ k = 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{R : Type.{u_4}} {R₂ : Type.{u_2}} {M : Type.{u_3}} {M₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 : Semiring.{u_4} R] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 : Semiring.{u_2} R₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 : AddCommMonoid.{u_3} M] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 : AddCommMonoid.{u_1} M₂] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 : Module.{u_4, u_3} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 : Module.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26] {σ₁₂ : RingHom.{u_4, u_2} R R₂ (Semiring.toNonAssocSemiring.{u_4} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11) (Semiring.toNonAssocSemiring.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14)} (p : Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (f : LinearMap.{u_4, u_2, u_3, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (h : forall (c : M), Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p (DFunLike.coe.{max (succ u_3) (succ u_1), succ u_3, succ u_1} (LinearMap.{u_4, u_2, u_3, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_4, u_2, u_3, u_1} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 σ₁₂) f c)) (x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.131 : R) (x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.133 : M), Eq.{succ u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x) (DFunLike.coe.{max (succ u_3) (succ u_1), succ u_3, succ u_1} (LinearMap.{u_4, u_2, u_3, u_1} R R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => M₂) (LinearMap.instFunLike.{u_4, u_2, u_3, u_1} R R₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 σ₁₂) f (HSMul.hSMul.{u_4, u_3, u_3} R M M (instHSMul.{u_4, u_3} R M (SMulZeroClass.toSMul.{u_4, u_3} R M (AddZero.toZero.{u_3} M (AddZeroClass.toAddZero.{u_3} M (AddMonoid.toAddZeroClass.{u_3} M (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20)))) (DistribSMul.toSMulZeroClass.{u_4, u_3} R M (AddMonoid.toAddZeroClass.{u_3} M (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20)) (DistribMulAction.toDistribSMul.{u_4, u_3} R M (MonoidWithZero.toMonoid.{u_4} R (Semiring.toMonoidWithZero.{u_4} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11)) (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20) (Module.toDistribMulAction.{u_4, u_3} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32))))) x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.131 x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.133)) (h (HSMul.hSMul.{u_4, u_3, u_3} R M M (instHSMul.{u_4, u_3} R M (SMulZeroClass.toSMul.{u_4, u_3} R M (AddZero.toZero.{u_3} M (AddZeroClass.toAddZero.{u_3} M (AddMonoid.toAddZeroClass.{u_3} M (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20)))) (DistribSMul.toSMulZeroClass.{u_4, u_3} R M (AddMonoid.toAddZeroClass.{u_3} M (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20)) (DistribMulAction.toDistribSMul.{u_4, u_3} R M (MonoidWithZero.toMonoid.{u_4} R (Semiring.toMonoidWithZero.{u_4} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11)) (AddCommMonoid.toAddMonoid.{u_3} M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20) (Module.toDistribMulAction.{u_4, u_3} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.32))))) x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.131 x._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.133))) (HSMul.hSMul.{u_2, u_1, u_1} R₂ (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (instHSMul.{u_2, u_1} R₂ (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (SMulZeroClass.toSMul.{u_2, u_1} R₂ (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (AddZero.toZero.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (AddZeroClass.toAddZero.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (AddMonoid.toAddZeroClass.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (AddCommMonoid.toAddMonoid.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (Submodule.addCommMonoid.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 p))))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R₂ (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (AddMonoid.toAddZeroClass.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (AddCommMonoid.toAddMonoid.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (Submodule.addCommMonoid.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 p))) (DistribMulAction.toDistribSMul.{u_2, u_1} R₂ (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (MonoidWithZero.toMonoid.{u_2} R₂ (Semiring.toMonoidWithZero.{u_2} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14)) (AddCommMonoid.toAddMonoid.{u_1} (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) (Submodule.addCommMonoid.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40 p)) (Module.toDistribMulAction.{u_2, u_1} R₂ (Subtype.{succ u_1} M₂ (fun (x : M₂) => Membership.mem.{u_1, u_1} M₂ (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) (SetLike.instMembership.{u_1, u_1} (Submodule.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40) M₂ (Submodule.setLike.{u_2, u_1} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.40)) p x)) inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.2251875111._hygCtx._hyg.14 (Submodule.addCommMonoid.{u_2, u_1} R₂ M₂ 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[inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.40 : Module.{u_3, u_7} R₂ M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.26] [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.44 : Module.{u_4, u_8} R₃ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.29] {σ₁₂ : RingHom.{u_1, u_3} R R₂ (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.11) (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.14)} {σ₂₃ : RingHom.{u_3, u_4} R₂ R₃ (Semiring.toNonAssocSemiring.{u_3} R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.14) (Semiring.toNonAssocSemiring.{u_4} R₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17)} {σ₁₃ : RingHom.{u_1, u_4} R R₃ (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.11) (Semiring.toNonAssocSemiring.{u_4} R₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17)} [inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.63 : RingHomCompTriple.{u_1, u_3, u_4} R R₂ R₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17 σ₁₂ σ₂₃ σ₁₃] (f : LinearMap.{u_1, u_3, u_5, u_7} R R₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.14 σ₁₂ M M₂ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.32 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.40) (g : LinearMap.{u_3, u_4, u_7, u_8} R₂ R₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17 σ₂₃ M₂ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.44) (p : Submodule.{u_4, u_8} R₃ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.29 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.44 σ₂₃) g b)), Eq.{max (succ u_5) (succ u_8)} (LinearMap.{u_1, u_4, u_5, u_8} R R₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17 σ₁₃ M (Subtype.{succ u_8} M₃ (fun (x : M₃) => Membership.mem.{u_8, u_8} M₃ (Submodule.{u_4, u_8} R₃ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.29 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.44) (SetLike.instMembership.{u_8, u_8} (Submodule.{u_4, u_8} R₃ M₃ inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1631029670._hygCtx._hyg.29 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inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.10 module_M)) p x)) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Subtype.{succ v} M (fun (x : M) => Membership.mem.{v, v} M (Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.10 module_M) (SetLike.instMembership.{v, v} (Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.10 module_M)) p x)) => M) (LinearMap.instFunLike.{u, u, v, v} R R (Subtype.{succ v} M (fun (x : M) => Membership.mem.{v, v} M (Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.10 module_M) (SetLike.instMembership.{v, v} (Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.10 module_M) M (Submodule.setLike.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.10 module_M)) p x)) M inst._@.Mathlib.Algebra.Module.Submodule.LinearMap.1704090140._hygCtx._hyg.7 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