diff --git "a/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.LocalizedModule.Exact.sym.json" "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.LocalizedModule.Exact.sym.json"
new file mode 100644--- /dev/null
+++ "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.LocalizedModule.Exact.sym.json"
@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["IsLocalizedModule","map_exact"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3 : CommSemiring.{u_1} R] (S : Submonoid.{u_1} R (MulZeroOneClass.toMulOneClass.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))))) {M₀ : Type.{u_2}} {M₀' : Type.{u_5}} [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 : AddCommMonoid.{u_2} M₀] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 : AddCommMonoid.{u_5} M₀'] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 : Module.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 : Module.{u_1, u_5} R M₀' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13] (f₀ : LinearMap.{u_1, u_1, u_2, u_5} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₀ M₀' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20) [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.33 : IsLocalizedModule.{u_1, u_2, u_5} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3 M₀ M₀' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 S f₀] {M₁ : Type.{u_3}} {M₁' : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 : AddCommMonoid.{u_3} M₁] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 : AddCommMonoid.{u_6} M₁'] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 : Module.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 : Module.{u_1, u_6} R M₁' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42] (f₁ : LinearMap.{u_1, u_1, u_3, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₁ M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49) [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.62 : IsLocalizedModule.{u_1, u_3, u_6} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3 M₁ M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 S f₁] {M₂ : Type.{u_4}} {M₂' : Type.{u_7}} [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68 : AddCommMonoid.{u_4} M₂] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 : AddCommMonoid.{u_7} M₂'] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.74 : Module.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78 : Module.{u_1, u_7} R M₂' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71] (f₂ : LinearMap.{u_1, u_1, u_4, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₂ M₂' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78) [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.91 : IsLocalizedModule.{u_1, u_4, u_7} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3 M₂ M₂' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78 S f₂] (g : LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45) (h : LinearMap.{u_1, u_1, u_3, u_4} R R 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(Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₀' M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_6} R R M₀' M₁' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)))) (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_3} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_6} R R R M₀' M₁' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 (smulCommClass_self.{u_1, u_6} R M₁' (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_6} R M₁' (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_6} M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42) (Module.toDistribMulAction.{u_1, u_6} R M₁' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49))))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45) => LinearMap.{u_1, u_1, u_5, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₀' M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49) (LinearMap.instFunLike.{u_1, u_1, max u_2 u_3, max u_5 u_6} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45) (LinearMap.{u_1, u_1, u_5, u_6} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₀' M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, u_5, u_6} R R M₀' M₁' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)))) (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_3} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, u_5, u_6} R R R M₀' M₁' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 (smulCommClass_self.{u_1, u_6} R M₁' (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_6} R M₁' (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_6} M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42) (Module.toDistribMulAction.{u_1, u_6} R M₁' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49)))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)))) (IsLocalizedModule.map.{u_1, u_2, u_5, u_3, u_6} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3 S M₀ M₀' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.20 f₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.33 M₁ M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 f₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.62) g)) (DFunLike.coe.{max (succ u_6) (succ u_7), succ u_6, succ u_7} (LinearMap.{u_1, u_1, u_6, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₁' M₂' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78) M₁' (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M₁') => M₂') (LinearMap.instFunLike.{u_1, u_1, u_6, u_7} R R M₁' M₂' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.74) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_3, u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₁ M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.74) => LinearMap.{u_1, u_1, u_6, u_7} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3))) M₁' M₂' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78) (LinearMap.instFunLike.{u_1, u_1, max u_3 u_4, max u_6 u_7} R R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)))) (LinearMap.module.{u_1, u_1, u_1, u_3, u_4} R R R M₁ M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.74)))) (LinearMap.module.{u_1, u_1, u_1, u_6, u_7} R R R M₁' M₂' (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78)))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3)))) (IsLocalizedModule.map.{u_1, u_3, u_6, u_4, u_7} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.3 S M₁ M₁' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.42 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.49 f₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.62 M₂ M₂' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.74 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.78 f₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.91) h)) (AddZero.toZero.{u_7} M₂' (AddZeroClass.toAddZero.{u_7} M₂' (AddMonoid.toAddZeroClass.{u_7} M₂' (AddCommMonoid.toAddMonoid.{u_7} M₂' inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331083._hygCtx._hyg.71)))))","typeFull":"∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M₀ : Type u_2} {M₀' : Type u_5} [inst_1 : AddCommMonoid M₀]\n  [inst_2 : AddCommMonoid M₀'] [inst_3 : Module R M₀] [inst_4 : Module R M₀'] (f₀ : M₀ →ₗ[R] M₀')\n  [inst_5 : IsLocalizedModule S f₀] {M₁ : Type u_3} {M₁' : Type u_6} [inst_6 : AddCommMonoid M₁]\n  [inst_7 : AddCommMonoid M₁'] [inst_8 : Module R M₁] [inst_9 : Module R M₁'] (f₁ : M₁ →ₗ[R] M₁')\n  [inst_10 : IsLocalizedModule S f₁] {M₂ : Type u_4} {M₂' : Type u_7} [inst_11 : AddCommMonoid M₂]\n  [inst_12 : AddCommMonoid M₂'] [inst_13 : Module R M₂] [inst_14 : Module R M₂'] (f₂ : M₂ →ₗ[R] M₂')\n  [inst_15 : IsLocalizedModule S f₂] (g : M₀ →ₗ[R] M₁) (h : M₁ →ₗ[R] M₂),\n  Function.Exact ⇑g ⇑h → Function.Exact ⇑((IsLocalizedModule.map S f₀ f₁) g) ⇑((IsLocalizedModule.map S f₁ f₂) h)","typeReadable":"∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M₀ : Type u_2} {M₀' : Type u_5} [inst_1 : AddCommMonoid M₀]\n  [inst_2 : AddCommMonoid M₀'] [inst_3 : Module R M₀] [inst_4 : Module R M₀'] (f₀ : M₀ →ₗ[R] M₀')\n  [inst_5 : IsLocalizedModule S f₀] {M₁ : Type u_3} {M₁' : Type u_6} [inst_6 : AddCommMonoid M₁]\n  [inst_7 : AddCommMonoid M₁'] [inst_8 : Module R M₁] [inst_9 : Module R M₁'] (f₁ : M₁ →ₗ[R] M₁')\n  [inst_10 : IsLocalizedModule S f₁] {M₂ : Type u_4} {M₂' : Type u_7} [inst_11 : AddCommMonoid M₂]\n  [inst_12 : AddCommMonoid M₂'] [inst_13 : Module R M₂] [inst_14 : Module R M₂'] (f₂ : M₂ →ₗ[R] M₂')\n  [inst_15 : IsLocalizedModule S f₂] (g : M₀ →ₗ[R] M₁) (h : M₁ →ₗ[R] M₂),\n  Function.Exact ⇑g ⇑h → Function.Exact ⇑((IsLocalizedModule.map S f₀ f₁) g) ⇑((IsLocalizedModule.map S f₁ f₂) h)","typeReferences":[["IsLocalizedModule"],["smulCommClass_self"],["LinearMap","instFunLike"],["CommMonoid","toMonoid"],["Module"],["CommSemiring"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["DistribMulAction","toMulAction"],["NonAssocSemiring","toMulZeroOneClass"],["IsLocalizedModule","map"],["CommSemiring","toSemiring"],["LinearMap","module"],["LinearMap"],["AddZeroClass","toAddZero"],["Function","Exact"],["CommSemiring","toCommMonoid"],["Submonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["OreLocalization","oreSetComm"],["AddCommMonoid","toAddMonoid"],["Function","Exact","of_ladder_linearEquiv_of_exact"],["Algebra","id"],["DFunLike","coe"],["LocalizedModule","mkLinearMap"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["IsScalarTower","right"],["Semiring","toModule"],["IsLocalizedModule","map_iso_commute"],["IsLocalizedModule","map"],["IsScalarTower","left"],["OreLocalization","instAddCommMonoidOreLocalization"],["LocalizedModule"],["CommSemiring","toSemiring"],["LinearMap","module"],["OreLocalization","instModuleOfIsScalarTower"],["Semiring","toMonoidWithZero"],["localizedModuleIsLocalizedModule"],["LinearMap"],["CommSemiring","toCommMonoid"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"],["IsLocalizedModule","iso"],["LocalizedModule","map_exact"]]},{"isProp":true,"kind":"theorem","name":["LocalizedModule","map_exact"],"typeFallback":"forall 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LinearMap.{u_1, u_1, max u_1 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.module.{u_1, u_1, u_1, u_2, u_3} R R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_3} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_2, max u_1 u_3} R R R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (smulCommClass_self.{u_1, max u_1 u_3} R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, max u_1 u_3} R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{max u_1 u_3} (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_3} R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))))))) (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) => LinearMap.{u_1, u_1, max u_1 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.instFunLike.{u_1, u_1, max u_2 u_3, max (max u_1 u_2) u_3} R R (LinearMap.{u_1, u_1, u_2, u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LinearMap.{u_1, u_1, max u_1 u_2, max u_1 u_3} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (LinearMap.addCommMonoid.{u_1, u_1, u_2, u_3} R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_1 u_2, max u_1 u_3} R R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_3} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_2, max u_1 u_3} R R R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_2} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R 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(OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) => LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (LinearMap.instFunLike.{u_1, u_1, max u_1 u_3, max u_1 u_4} R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (smulCommClass_self.{u_1, u_4} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_3, max u_1 u_4} R R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (smulCommClass_self.{u_1, max u_1 u_4} R (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, max u_1 u_4} R (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (Module.toDistribMulAction.{u_1, max u_1 u_4} R (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))))))) (LinearMap.{u_1, u_1, u_3, u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₁ M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_3, u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₁ M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) => LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.instFunLike.{u_1, u_1, max u_3 u_4, max (max u_1 u_3) u_4} R R (LinearMap.{u_1, u_1, u_3, u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₁ M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_4} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (LinearMap.addCommMonoid.{u_1, u_1, u_3, u_4} R R M₁ M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_1 u_3, max u_1 u_4} R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (smulCommClass_self.{u_1, u_4} R M₂ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_3, max u_1 u_4} R R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (smulCommClass_self.{u_1, max u_1 u_4} R (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, max u_1 u_4} R (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{max u_1 u_4} (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (Module.toDistribMulAction.{u_1, max u_1 u_4} R (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))))))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (IsLocalizedModule.map.{u_1, u_3, max u_1 u_3, u_4, max u_1 u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_3} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.mkLinearMap.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (localizedModuleIsLocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) M₂ (LocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_4, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.mkLinearMap.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74) (localizedModuleIsLocalizedModule.{u_1, u_4} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74)) h)) (OreLocalization.instZero.{u_1, u_4} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₂ (AddZero.toZero.{u_4} M₂ (AddZeroClass.toAddZero.{u_4} M₂ (AddMonoid.toAddZeroClass.{u_4} M₂ (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68)))) (DistribMulAction.toMulAction.{u_1, u_4} R M₂ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_4} M₂ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68) (Module.toDistribMulAction.{u_1, u_4} R M₂ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.68 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.74))))","typeFull":"∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M₀ : Type u_2} [inst_1 : AddCommMonoid M₀]\n  [inst_2 : Module R M₀] {M₁ : Type u_3} [inst_3 : AddCommMonoid M₁] [inst_4 : Module R M₁] {M₂ : Type u_4}\n  [inst_5 : AddCommMonoid M₂] [inst_6 : Module R M₂] (g : M₀ →ₗ[R] M₁) (h : M₁ →ₗ[R] M₂),\n  Function.Exact ⇑g ⇑h →\n    Function.Exact ⇑((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₀) (LocalizedModule.mkLinearMap S M₁)) g)\n      ⇑((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₁) (LocalizedModule.mkLinearMap S M₂)) h)","typeReadable":"∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M₀ : Type u_2} [inst_1 : AddCommMonoid M₀]\n  [inst_2 : Module R M₀] {M₁ : Type u_3} [inst_3 : AddCommMonoid M₁] [inst_4 : Module R M₁] {M₂ : Type u_4}\n  [inst_5 : AddCommMonoid M₂] [inst_6 : Module R M₂] (g : M₀ →ₗ[R] M₁) (h : M₁ →ₗ[R] M₂),\n  Function.Exact ⇑g ⇑h →\n    Function.Exact ⇑((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₀) (LocalizedModule.mkLinearMap S M₁)) g)\n      ⇑((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₁) (LocalizedModule.mkLinearMap S M₂)) 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{R : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 : CommSemiring.{u_1} R] (S : Submonoid.{u_1} R (MulZeroOneClass.toMulOneClass.{u_1} R (NonAssocSemiring.toMulZeroOneClass.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))))) {M₀ : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 : AddCommMonoid.{u_3} M₀] [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 : Module.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10] {M₁ : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 : AddCommMonoid.{u_2} M₁] 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.module.{u_1, u_1, u_1, u_3, u_2} R R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_2} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (CommMonoid.toMonoid.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (smulCommClass_self.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))))))) (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.instFunLike.{u_1, u_1, max u_3 u_2, max (max u_1 u_3) u_2} R R (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_2} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_3, max u_1 u_2} R R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))))))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (IsLocalizedModule.map.{u_1, u_3, max u_1 u_3, u_2, max u_1 u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.mkLinearMap.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (localizedModuleIsLocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) M₁ (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.mkLinearMap.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (localizedModuleIsLocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) g))) y) -> Prop) (x._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx.176.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.184 : Membership.mem.{max u_1 u_2, max u_1 u_2} (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (Set.{max u_1 u_2} (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (Set.instMembership.{max u_1 u_2} (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (Set.range.{max u_1 u_2, succ (max u_1 u_3)} (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (DFunLike.coe.{max (max (succ u_1) (succ u_3)) (succ u_2), max (succ u_1) (succ u_3), max (succ u_1) (succ u_2)} (LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.module.{u_1, u_1, u_1, u_3, u_2} R R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_3, max u_1 u_2} R R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R 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(MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (smulCommClass_self.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))))))) (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) => LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.instFunLike.{u_1, u_1, max u_3 u_2, max (max u_1 u_3) u_2} R R (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (LinearMap.addCommMonoid.{u_1, u_1, u_3, u_2} R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R 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(OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_2} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_3, max u_1 u_2} R R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))))))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (IsLocalizedModule.map.{u_1, u_3, max u_1 u_3, u_2, max u_1 u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.mkLinearMap.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (localizedModuleIsLocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) M₁ (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.module.{u_1, u_1, u_1, u_3, u_2} R R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_3, max u_1 u_2} R R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (smulCommClass_self.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))))))) (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) => LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.instFunLike.{u_1, u_1, max u_3 u_2, max (max u_1 u_3) u_2} R R (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (LinearMap.addCommMonoid.{u_1, u_1, u_3, u_2} R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) 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(OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_2} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_3, max u_1 u_2} R R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.mkLinearMap.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (localizedModuleIsLocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) M₁ (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) => LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LinearMap.instFunLike.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 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M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.module.{u_1, u_1, u_1, u_3, u_2} R R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_2} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_2} M₁ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (smulCommClass_self.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))))))) (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.instFunLike.{u_1, u_1, max u_3 u_2, max (max u_1 u_3) u_2} R R (LinearMap.{u_1, u_1, u_3, u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) M₀ M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (LinearMap.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (LinearMap.addCommMonoid.{u_1, u_1, u_3, u_2} R R M₀ M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (LinearMap.addCommMonoid.{u_1, u_1, max u_1 u_3, max u_1 u_2} R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (smulCommClass_self.{u_1, u_2} R M₁ (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (CommMonoid.toMonoid.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)))) (LinearMap.module.{u_1, u_1, u_1, max u_1 u_3, max u_1 u_2} R R R (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) 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inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (Module.toDistribMulAction.{u_1, max u_1 u_2} R (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))))))) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)))) (IsLocalizedModule.map.{u_1, u_3, max u_1 u_3, u_2, max u_1 u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ (LocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_3} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_3, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_3} R M₀ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_3} M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10) (Module.toDistribMulAction.{u_1, u_3} R M₀ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.mkLinearMap.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) (localizedModuleIsLocalizedModule.{u_1, u_3} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₀ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.16) M₁ (LocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (OreLocalization.instAddCommMonoidOreLocalization.{u_1, u_2} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (OreLocalization.instModuleOfIsScalarTower.{u_1, u_2, u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S (OreLocalization.oreSetComm.{u_1} R (CommSemiring.toCommMonoid.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) S) M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45 (Semiring.toModule.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3)) (IsScalarTower.left.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (DistribMulAction.toMulAction.{u_1, u_2} R M₁ (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (AddCommMonoid.toAddMonoid.{u_2} M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39) (Module.toDistribMulAction.{u_1, u_2} R M₁ (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45))) (IsScalarTower.right.{u_1, u_1} R R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 (CommSemiring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3) (Algebra.id.{u_1} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3))) (LocalizedModule.mkLinearMap.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45) (localizedModuleIsLocalizedModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.3 S M₁ inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.39 inst._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.45)) g) y_1) y) x hx)) -> (motive x._@.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx.176.Mathlib.Algebra.Module.LocalizedModule.Exact.1214331082._hygCtx._hyg.184)","typeFull":"∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M₀ : Type u_3} [inst_1 : AddCommMonoid M₀]\n  [inst_2 : Module R M₀] {M₁ : Type u_2} [inst_3 : AddCommMonoid M₁] [inst_4 : Module R M₁] (g : M₀ →ₗ[R] M₁)\n  (y : LocalizedModule S M₁)\n  (motive :\n    y ∈ Set.range ⇑((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₀) (LocalizedModule.mkLinearMap S M₁)) g) →\n      Prop)\n  (x :\n    y ∈ Set.range ⇑((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₀) (LocalizedModule.mkLinearMap S M₁)) g)),\n  (∀ (x : LocalizedModule S M₀)\n      (hx : ((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₀) (LocalizedModule.mkLinearMap S M₁)) g) x = y),\n      motive ⋯) →\n    motive x","typeReadable":"∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) {M₀ : Type u_3} [inst_1 : AddCommMonoid M₀]\n  [inst_2 : Module R M₀] {M₁ : Type u_2} [inst_3 : AddCommMonoid M₁] [inst_4 : Module R M₁] (g : M₀ →ₗ[R] M₁)\n  (y : LocalizedModule S M₁)\n  (motive :\n    y ∈ Set.range ⇑((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₀) (LocalizedModule.mkLinearMap S M₁)) g) →\n      Prop)\n  (x :\n    y ∈ Set.range ⇑((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₀) (LocalizedModule.mkLinearMap S M₁)) g)),\n  (∀ (x : LocalizedModule S M₀)\n      (hx : ((IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M₀) (LocalizedModule.mkLinearMap S M₁)) g) x = y),\n      motive ⋯) →\n    motive x","typeReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["Module"],["OreLocalization","oreSetComm"],["Membership","mem"],["CommSemiring"],["Exists","intro"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["Algebra","id"],["DFunLike","coe"],["Set","range"],["LocalizedModule","mkLinearMap"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["IsScalarTower","right"],["Eq"],["Semiring","toModule"],["NonAssocSemiring","toMulZeroOneClass"],["IsLocalizedModule","map"],["LocalizedModule"],["OreLocalization","instAddCommMonoidOreLocalization"],["IsScalarTower","left"],["Set"],["LinearMap","module"],["CommSemiring","toSemiring"],["OreLocalization","instModuleOfIsScalarTower"],["Semiring","toMonoidWithZero"],["localizedModuleIsLocalizedModule"],["LinearMap"],["CommSemiring","toCommMonoid"],["Set","instMembership"],["LinearMap","addCommMonoid"],["Submonoid"],["Module","toDistribMulAction"]],"valueReferences":[["smulCommClass_self"],["CommMonoid","toMonoid"],["LinearMap","instFunLike"],["OreLocalization","oreSetComm"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Algebra","id"],["LocalizedModule","mkLinearMap"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["IsScalarTower","right"],["Eq"],["Semiring","toModule"],["IsLocalizedModule","map"],["OreLocalization","instAddCommMonoidOreLocalization"],["LocalizedModule"],["IsScalarTower","left"],["CommSemiring","toSemiring"],["LinearMap","module"],["OreLocalization","instModuleOfIsScalarTower"],["Semiring","toMonoidWithZero"],["localizedModuleIsLocalizedModule"],["LinearMap"],["CommSemiring","toCommMonoid"],["Exists","casesOn"],["LinearMap","addCommMonoid"],["Module","toDistribMulAction"]]}]