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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Group.Finset.Powerset.sym.json

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+[{"isProp":true,"kind":"theorem","name":["Finset","sum_powerset_cons"],"typeFallback":"forall {α : Type.{u_1}} {β : Type.{u_2}} {s : Finset.{u_1} α} {a : α} [inst._@.Mathlib.Algebra.BigOperators.Group.Finset.Powerset.226710504._hygCtx._hyg.8 : AddCommMonoid.{u_2} β] (ha : Not (Membership.mem.{u_1, u_1} α (Finset.{u_1} α) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} α) α (Finset.instSetLike.{u_1} α)) s a)) (f : (Finset.{u_1} α) -> β), Eq.{succ u_2} β (Finset.sum.{u_1, u_2} (Finset.{u_1} α) β inst._@.Mathlib.Algebra.BigOperators.Group.Finset.Powerset.226710504._hygCtx._hyg.8 (Finset.powerset.{u_1} α (Finset.cons.{u_1} α a s ha)) (fun (t : Finset.{u_1} α) => f t)) (HAdd.hAdd.{u_2, u_2, u_2} β β β (instHAdd.{u_2} β (AddZero.toAdd.{u_2} β (AddZeroClass.toAddZero.{u_2} β (AddMonoid.toAddZeroClass.{u_2} β (AddCommMonoid.toAddMonoid.{u_2} β inst._@.Mathlib.Algebra.BigOperators.Group.Finset.Powerset.226710504._hygCtx._hyg.8))))) (Finset.sum.{u_1, u_2} (Finset.{u_1} α) β 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Ext.Finite.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.NatPowAssoc.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.PUnit.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Submonoid.Finsupp.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Equiv.sym.json

@@ -0,0 +1 @@
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u_2} G H (MulZeroClass.toMul.{u_1} G (MulZeroOneClass.toMulZeroClass.{u_1} G inst._@.Mathlib.Algebra.GroupWithZero.Equiv.3135041319._hygCtx._hyg.4)) (MulZeroClass.toMul.{u_2} H (MulZeroOneClass.toMulZeroClass.{u_2} H inst._@.Mathlib.Algebra.GroupWithZero.Equiv.3135041319._hygCtx._hyg.7)))) f x)","typeFull":"∀ {G : Type u_1} {H : Type u_2} [inst : MulZeroOneClass G] [inst_1 : MulZeroOneClass H] (f : G ≃* H) (x : G),\n  f.toMonoidWithZeroHom x = f x","typeReadable":"∀ {G : Type u_1} {H : Type u_2} [inst : MulZeroOneClass G] [inst_1 : MulZeroOneClass H] (f : G ≃* H) (x : G),\n  f.toMonoidWithZeroHom x = f 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[inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.7 : MulZeroOneClass.{u_2} H] {f : MulEquiv.{u_1, u_2} G H (MulZeroClass.toMul.{u_1} G (MulZeroOneClass.toMulZeroClass.{u_1} G inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.4)) (MulZeroClass.toMul.{u_2} H (MulZeroOneClass.toMulZeroClass.{u_2} H inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.7))} {g : MulEquiv.{u_1, u_2} G H (MulZeroClass.toMul.{u_1} G (MulZeroOneClass.toMulZeroClass.{u_1} G inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.4)) (MulZeroClass.toMul.{u_2} H (MulZeroOneClass.toMulZeroClass.{u_2} H inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.7))}, Eq.{1} Prop (Eq.{max (succ u_1) (succ u_2)} (MonoidWithZeroHom.{u_1, u_2} G H inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.4 inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.7) (MulEquiv.toMonoidWithZeroHom.{u_1, u_2} G H inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.4 inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.7 f) (MulEquiv.toMonoidWithZeroHom.{u_1, u_2} G H inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.4 inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.7 g)) (Eq.{max (succ u_1) (succ u_2)} (MulEquiv.{u_1, u_2} G H (MulZeroClass.toMul.{u_1} G (MulZeroOneClass.toMulZeroClass.{u_1} G inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.4)) (MulZeroClass.toMul.{u_2} H (MulZeroOneClass.toMulZeroClass.{u_2} H inst._@.Mathlib.Algebra.GroupWithZero.Equiv.758429159._hygCtx._hyg.7))) f g)","typeFull":"∀ {G : Type u_1} {H : Type u_2} [inst : MulZeroOneClass G] [inst_1 : MulZeroOneClass H] {f g : G ≃* H},\n  (f.toMonoidWithZeroHom = g.toMonoidWithZeroHom) = (f = g)","typeReadable":"∀ {G : Type u_1} {H : Type u_2} [inst : MulZeroOneClass G] [inst_1 : MulZeroOneClass H] {f g : G ≃* H},\n  (f.toMonoidWithZeroHom = g.toMonoidWithZeroHom) = (f = g)","typeReferences":[["MulEquiv"],["MulZeroOneClass","toMulZeroClass"],["MonoidWithZeroHom"],["MulZeroClass","toMul"],["MulZeroOneClass"],["MulEquiv","toMonoidWithZeroHom"],["Eq"]],"valueReferences":[["MulEquiv"],["MulZeroOneClass","toMulZeroClass"],["MulEquiv","toMonoidWithZeroHom_inj"],["MonoidWithZeroHom"],["MulZeroClass","toMul"],["MulEquiv","toMonoidWithZeroHom"],["Eq"],["propext"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","GroupWithZero","Equiv",0,"MulEquiv","toMonoidWithZeroHom_inj","_simp_1_2"],"typeFallback":"forall {M : Type.{u_4}} {N : Type.{u_5}} [inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 : Mul.{u_4} M] [inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18 : Mul.{u_5} N] {f : MulEquiv.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18} {g : MulEquiv.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18}, Eq.{1} Prop (Eq.{max (succ u_4) (succ u_5)} (MulEquiv.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18) f g) (forall (x : M), Eq.{succ u_5} N (DFunLike.coe.{max (succ u_4) (succ u_5), succ u_4, succ u_5} (MulEquiv.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => N) (EquivLike.toFunLike.{max (succ u_4) (succ u_5), succ u_4, succ u_5} (MulEquiv.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18) M N (MulEquiv.instEquivLike.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18)) f x) (DFunLike.coe.{max (succ u_4) (succ u_5), succ u_4, succ u_5} (MulEquiv.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => N) (EquivLike.toFunLike.{max (succ u_4) (succ u_5), succ u_4, succ u_5} (MulEquiv.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18) M N (MulEquiv.instEquivLike.{u_4, u_5} M N inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Group.Equiv.Defs.722126854._hygCtx._hyg.18)) g x))","typeFull":"∀ {M : Type u_4} {N : Type u_5} [inst : Mul M] [inst_1 : Mul N] {f g : M ≃* N}, (f = g) = ∀ (x : M), f x = g x","typeReadable":"∀ {M 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.NoZeroSMulDivisors.Defs.sym.json

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NoZeroSMulDivisors.{0, u_3} Int G (MulZeroClass.toZero.{0} Int (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Int (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Int (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} Int (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} Int (CommRing.toNonUnitalCommRing.{0} Int Int.instCommRing)))))) (NegZeroClass.toZero.{u_3} G (SubNegZeroMonoid.toNegZeroClass.{u_3} G (SubtractionMonoid.toSubNegZeroMonoid.{u_3} G (AddGroup.toSubtractionMonoid.{u_3} G inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.3656678229._hygCtx._hyg.5)))) (SubNegMonoid.toZSMul.{u_3} G (AddGroup.toSubNegMonoid.{u_3} G inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.3656678229._hygCtx._hyg.5))","typeFull":"∀ {G : Type u_3} [inst : AddGroup G] [IsAddTorsionFree G], NoZeroSMulDivisors ℤ G","typeReadable":"∀ {G : Type u_3} [inst : AddGroup G] [IsAddTorsionFree G], NoZeroSMulDivisors ℤ 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[NoZeroSMulDivisors R M], Module.IsTorsionFree R M","typeReferences":[["Module","IsTorsionFree"],["SubtractionMonoid","toSubNegZeroMonoid"],["Module"],["AddCommGroup","toAddGroup"],["IsDomain"],["SubtractionCommMonoid","toSubtractionMonoid"],["SMulZeroClass","toSMul"],["SubNegZeroMonoid","toNegZeroClass"],["NoZeroSMulDivisors"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["AddGroup","toSubNegMonoid"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["AddCommGroup","toDivisionAddCommMonoid"],["SubNegMonoid","toAddMonoid"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["NegZeroClass","toZero"],["AddCommGroup","toAddCommMonoid"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["SubtractionMonoid","toSubNegZeroMonoid"],["IsRegular","ne_zero"],["sub_eq_zero"],["_private","Mathlib","Algebra","NoZeroSMulDivisors","Defs",0,"instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors","_simp_1"],["Eq","trans"],["Eq","mp"],["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["SubNegZeroMonoid","toNegZeroClass"],["AddGroup","toSubtractionMonoid"],["Module","IsTorsionFree","mk"],["congrArg"],["Semiring","toNonAssocSemiring"],["Or"],["SubNegMonoid","toSub"],["congr"],["MonoidWithZero","toMonoid"],["Eq","symm"],["HSub","hSub"],["instHSMul"],["Zero","toOfNat0"],["AddGroup","toSubNegMonoid"],["Eq"],["NoZeroSMulDivisors","eq_zero_or_eq_zero_of_smul_eq_zero"],["propext"],["DistribSMul","toSMulZeroClass"],["IsDomain","toNontrivial"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["smul_sub"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["false_or"],["SubNegMonoid","toAddMonoid"],["MulZeroClass","toZero"],["eq_false"],["HSMul","hSMul"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["AddCommGroup","toAddCommMonoid"],["NegZeroClass","toZero"],["False"],["instHSub"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["noZeroSMulDivisors_iff_right_eq_zero_of_smul"],"typeFallback":"forall 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0","typeReferences":[["SMul"],["Iff"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Ne"],["Zero"],["Eq"],["OfNat","ofNat"],["NoZeroSMulDivisors"]],"valueReferences":[["_private","Mathlib","Algebra","NoZeroSMulDivisors","Defs",0,"noZeroSMulDivisors_iff_right_eq_zero_of_smul","_simp_1_2"],["implies_congr"],["Not"],["_private","Mathlib","Algebra","NoZeroSMulDivisors","Defs",0,"noZeroSMulDivisors_iff_right_eq_zero_of_smul","_simp_1_1"],["NoZeroSMulDivisors"],["OfNat","ofNat"],["Iff","intro"],["congrArg"],["Or"],["Eq","refl"],["Iff"],["forall_congr"],["HSMul","hSMul"],["id"],["instHSMul"],["Eq","mpr"],["Ne"],["Zero","toOfNat0"],["congrFun'"],["Eq"]]},{"isProp":true,"kind":"theorem","name":["noZeroSMulDivisors_iff"],"typeFallback":"forall (R : Type.{u_4}) (M : Type.{u_5}) [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10 : Zero.{u_4} R] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13 : Zero.{u_5} M] 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: Type u_5) [inst : Zero R] [inst_1 : Zero M] [inst_2 : SMul R M],\n  NoZeroSMulDivisors R M ↔ ∀ {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0","typeReadable":"∀ (R : Type u_4) (M : Type u_5) [inst : Zero R] [inst_1 : Zero M] [inst_2 : SMul R M],\n  NoZeroSMulDivisors R M ↔ ∀ {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0","typeReferences":[["SMul"],["Or"],["Iff"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Zero"],["Eq"],["OfNat","ofNat"],["NoZeroSMulDivisors"]],"valueReferences":[["NoZeroSMulDivisors","casesOn"],["Or"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Eq"],["NoZeroSMulDivisors","mk"],["OfNat","ofNat"],["NoZeroSMulDivisors"],["Iff","intro"]]},{"isProp":false,"kind":"definition","name":["NoZeroSMulDivisors","casesOn"],"typeFallback":"forall {R : Type.{u_4}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10 : Zero.{u_4} R] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13 : Zero.{u_5} M] 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• x = 0 → c = 0 ∨ x = 0) → motive ⋯) →\n                motive t","typeReadable":"{R : Type u_4} →\n  {M : Type u_5} →\n    [inst : Zero R] →\n      [inst_1 : Zero M] →\n        [inst_2 : SMul R M] →\n          {motive : NoZeroSMulDivisors R M → Sort u} →\n            (t : NoZeroSMulDivisors R M) →\n              ((eq_zero_or_eq_zero_of_smul_eq_zero : ∀ {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0) → motive ⋯) →\n                motive t","typeReferences":[["SMul"],["Or"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Zero"],["Eq"],["NoZeroSMulDivisors","mk"],["OfNat","ofNat"],["NoZeroSMulDivisors"]],"valueReferences":[["NoZeroSMulDivisors","rec"]]},{"isProp":false,"kind":"recursor","name":["NoZeroSMulDivisors","rec"],"typeFallback":"forall {R : Type.{u_4}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10 : Zero.{u_4} R] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13 : Zero.{u_5} M] 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NoZeroSMulDivisors R M) → motive t","typeReadable":"{R : Type u_4} →\n  {M : Type u_5} →\n    [inst : Zero R] →\n      [inst_1 : Zero M] →\n        [inst_2 : SMul R M] →\n          {motive : NoZeroSMulDivisors R M → Sort u} →\n            ((eq_zero_or_eq_zero_of_smul_eq_zero : ∀ {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0) → motive ⋯) →\n              (t : NoZeroSMulDivisors R M) → motive t","typeReferences":[["SMul"],["Or"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Zero"],["Eq"],["NoZeroSMulDivisors","mk"],["OfNat","ofNat"],["NoZeroSMulDivisors"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["NoZeroSMulDivisors","recOn"],"typeFallback":"forall {R : Type.{u_4}} {M : Type.{u_5}} [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10 : Zero.{u_4} R] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13 : Zero.{u_5} M] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.16 : SMul.{u_4, u_5} R 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[inst_1 : Zero M] →\n        [inst_2 : SMul R M] →\n          {motive : NoZeroSMulDivisors R M → Sort u} →\n            (t : NoZeroSMulDivisors R M) →\n              ((eq_zero_or_eq_zero_of_smul_eq_zero : ∀ {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0) → motive ⋯) →\n                motive t","typeReferences":[["SMul"],["Or"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Zero"],["Eq"],["NoZeroSMulDivisors","mk"],["OfNat","ofNat"],["NoZeroSMulDivisors"]],"valueReferences":[["NoZeroSMulDivisors","rec"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","NoZeroSMulDivisors","Defs",0,"noZeroSMulDivisors_iff_right_eq_zero_of_smul","_simp_1_1"],"typeFallback":"forall (R : Type.{u_4}) (M : Type.{u_5}) [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10 : Zero.{u_4} R] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13 : Zero.{u_5} M] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.16 : 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NoZeroSMulDivisors R M = ∀ {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0","typeReadable":"∀ (R : Type u_4) (M : Type u_5) [inst : Zero R] [inst_1 : Zero M] [inst_2 : SMul R M],\n  NoZeroSMulDivisors R M = ∀ {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0","typeReferences":[["SMul"],["Or"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Zero"],["Eq"],["OfNat","ofNat"],["NoZeroSMulDivisors"]],"valueReferences":[["noZeroSMulDivisors_iff"],["Or"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Eq"],["OfNat","ofNat"],["NoZeroSMulDivisors"],["propext"]]},{"isProp":true,"kind":"theorem","name":["NoZeroSMulDivisors","eq_zero_or_eq_zero_of_smul_eq_zero"],"typeFallback":"forall {R : Type.{u_4}} {M : Type.{u_5}} {inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10 : Zero.{u_4} R} {inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13 : Zero.{u_5} M} {inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.16 : SMul.{u_4, u_5} R M} [self : NoZeroSMulDivisors.{u_4, u_5} R M inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10 inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13 inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.16] {c : R} {x : M}, (Eq.{succ u_5} M (HSMul.hSMul.{u_4, u_5, u_5} R M M (instHSMul.{u_4, u_5} R M inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.16) c x) (OfNat.ofNat.{u_5} M 0 (Zero.toOfNat0.{u_5} M inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13))) -> (Or (Eq.{succ u_4} R c (OfNat.ofNat.{u_4} R 0 (Zero.toOfNat0.{u_4} R inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10))) (Eq.{succ u_5} M x (OfNat.ofNat.{u_5} M 0 (Zero.toOfNat0.{u_5} M inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13))))","typeFull":"∀ {R : Type u_4} {M : Type u_5} {inst : Zero R} {inst_1 : Zero M} {inst_2 : SMul R M} [self : NoZeroSMulDivisors R M]\n  {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0","typeReadable":"∀ {R : Type u_4} {M : Type u_5} {inst : Zero R} {inst_1 : Zero M} {inst_2 : SMul R M} [self : NoZeroSMulDivisors R M]\n  {c : R} {x : M}, c • x = 0 → c = 0 ∨ x = 0","typeReferences":[["SMul"],["Or"],["HSMul","hSMul"],["instHSMul"],["Zero","toOfNat0"],["Zero"],["Eq"],["OfNat","ofNat"],["NoZeroSMulDivisors"]],"valueReferences":[]},{"isProp":false,"kind":"inductive","name":["NoZeroSMulDivisors"],"typeFallback":"forall (R : Type.{u_4}) (M : Type.{u_5}) [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.10 : Zero.{u_4} R] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.13 : Zero.{u_5} M] [inst._@.Mathlib.Algebra.NoZeroSMulDivisors.Defs.1771869601._hygCtx._hyg.16 : SMul.{u_4, u_5} R M], Prop","typeFull":"(R : Type u_4) → (M : Type u_5) → [Zero R] → [Zero M] → [SMul R M] → Prop","typeReadable":"(R : Type u_4) → (M : Type u_5) → [Zero R] → [Zero M] → [SMul R M] → 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Ring.MinimalAxioms.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicTopology.SimplicialSet.Finite.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Complex.BorelCaratheodory.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Complex.Cardinality.sym.json

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