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- .gitattributes +108 -0
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[{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","Central","Basic",0,"Algebra","IsCentral","baseField_essentially_unique","_simp_1_1"],"typeFallback":"forall {α : Type.{u}} {ι : Sort.{u_1}} {f : ι -> α} {x : α}, Eq.{1} Prop (Membership.mem.{u, u} α (Set.{u} α) (Set.instMembership.{u} α) (Set.range.{u, u_1} α ι f) x) (Exists.{u_1} ι (fun (y : ι) => Eq.{succ u} α (f y) x))","typeFull":"∀ {α : Type u} {ι : Sort u_1} {f : ι → α} {x : α}, (x ∈ Set.range f) = ∃ y, f y = x","typeReadable":"∀ {α : Type u} {ι : Sort u_1} {f : ι → α} {x : α}, (x ∈ Set.range f) = ∃ y, f y = 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⋯","typeReferences":[["Exists"],["Exists","intro"],["Eq"]],"valueReferences":[["Exists"],["Exists","intro"],["forall_exists_index"],["propext"]]},{"isProp":true,"kind":"theorem","name":["Algebra","IsCentral","baseField_essentially_unique"],"typeFallback":"forall (k : Type.{u_1}) (K : Type.{u_2}) (D : Type.{u_3}) [inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.28 : Field.{u_1} k] [inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.31 : Field.{u_2} K] [inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.34 : Ring.{u_3} D] [inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.37 : Nontrivial.{u_3} D] [inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.40 : Algebra.{u_1, u_2} k K (Semifield.toCommSemiring.{u_1} k (Field.toSemifield.{u_1} k inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.28)) (DivisionSemiring.toSemiring.{u_2} K (Semifield.toDivisionSemiring.{u_2} K (Field.toSemifield.{u_2} K 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(Semifield.toDivisionSemiring.{u_2} K (Field.toSemifield.{u_2} K inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.31))) inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.40) (Algebra.toSMul.{u_2, u_3} K D (Semifield.toCommSemiring.{u_2} K (Field.toSemifield.{u_2} K inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.31)) (Ring.toSemiring.{u_3} D inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.34) inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.44) (Algebra.toSMul.{u_1, u_3} k D (Semifield.toCommSemiring.{u_1} k (Field.toSemifield.{u_1} k inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.28)) (Ring.toSemiring.{u_3} D inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.34) inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.48)] [inst._@.Mathlib.Algebra.Central.Basic.3983489039._hygCtx._hyg.57 : Algebra.IsCentral.{u_1, u_3} k (Semifield.toCommSemiring.{u_1} k (Field.toSemifield.{u_1} k 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inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.11) (Lattice.toSemilatticeSup.{u_1} (Subalgebra.{u_2, u_1} K D inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.11) (CompleteLattice.toLattice.{u_1} (Subalgebra.{u_2, u_1} K D inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.11) (Algebra.instCompleteLatticeSubalgebra.{u_2, u_1} K D inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Central.Basic.578372411._hygCtx._hyg.11)))))) (CompleteLattice.toBoundedOrder.{u_1} (Subalgebra.{u_2, 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inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.21 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.11)) (AlgEquiv.symm.{u_2, u_1, u_1} K D D' inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.21 e) x)) -> Prop) (x._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.63 : Membership.mem.{u_1, u_1} D (Subalgebra.{u_2, u_1} K D inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Basic.2947200217._hygCtx._hyg.8 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.CharP.Reduced.sym.json
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Semiconj.Units.sym.json
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[{"isProp":true,"kind":"theorem","name":["AddSemiconjBy","addUnits_neg_right_iff","_simp_1"],"typeFallback":"forall {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3 : AddMonoid.{u_1} M] {a : M} {x : AddUnits.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3} {y : AddUnits.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3}, Eq.{1} Prop (AddSemiconjBy.{u_1} M (AddZero.toAdd.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3))) a (AddUnits.val.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3 (Neg.neg.{u_1} (AddUnits.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3) (AddUnits.instNeg.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3) x)) (AddUnits.val.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3 (Neg.neg.{u_1} (AddUnits.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3) (AddUnits.instNeg.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3) y))) (AddSemiconjBy.{u_1} M (AddZero.toAdd.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3))) a (AddUnits.val.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3 x) (AddUnits.val.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2851327928._hygCtx._hyg.3 y))","typeFull":"∀ {M : Type u_1} [inst : AddMonoid M] {a : M} {x y : AddUnits M}, AddSemiconjBy a ↑(-x) ↑(-y) = AddSemiconjBy a ↑x ↑y","typeReadable":"∀ {M : Type u_1} [inst : AddMonoid M] {a : M} {x y : AddUnits M}, AddSemiconjBy a ↑(-x) ↑(-y) = AddSemiconjBy a ↑x ↑y","typeReferences":[["AddUnits"],["Neg","neg"],["AddUnits","instNeg"],["AddUnits","val"],["AddMonoid"],["AddSemiconjBy"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["Eq"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["AddUnits"],["Neg","neg"],["AddUnits","instNeg"],["AddUnits","val"],["AddSemiconjBy","addUnits_neg_right_iff"],["AddSemiconjBy"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["propext"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","Group","Semiconj","Units",0,"SemiconjBy","units_zpow_right","_simp_1_4"],"typeFallback":"forall {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Group.Semiconj.Units.2798346735._hygCtx._hyg.3 : Monoid.{u_1} M] {a : M} {x : Units.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2798346735._hygCtx._hyg.3} {y : Units.{u_1} M inst._@.Mathlib.Algebra.Group.Semiconj.Units.2798346735._hygCtx._hyg.3}, (SemiconjBy.{u_1} M (MulOne.toMul.{u_1} M (MulOneClass.toMulOne.{u_1} M 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[inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.8 : SMul.{u_1, u_3} R M] [inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.12 : SMul.{u_1, u_2} R S] [inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.16 : SMul.{u_2, u_3} S M] [inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.20 : IsScalarTower.{u_1, u_2, u_3} R S M inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.12 inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.8] (a : R), (IsSMulRegular.{u_2, u_3} S M inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.16 (HSMul.hSMul.{u_1, u_2, u_2} R S S (instHSMul.{u_1, u_2} R S inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.12) a s)) -> (IsSMulRegular.{u_2, u_3} S M inst._@.Mathlib.Algebra.Regular.SMul.3428064138._hygCtx._hyg.16 s)","typeFull":"∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} {s : S} [inst : SMul R M] [inst_1 : SMul R S] 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inst._@.Mathlib.Algebra.Regular.SMul.4090659483._hygCtx._hyg.25) inst._@.Mathlib.Algebra.Regular.SMul.4090659483._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Regular.SMul.4090659483._hygCtx._hyg.8], (IsSMulRegular.{u_1, u_3} R M inst._@.Mathlib.Algebra.Regular.SMul.4090659483._hygCtx._hyg.8 a) -> (Iff (IsSMulRegular.{u_1, u_3} R M inst._@.Mathlib.Algebra.Regular.SMul.4090659483._hygCtx._hyg.8 (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R inst._@.Mathlib.Algebra.Regular.SMul.4090659483._hygCtx._hyg.25) a b)) (IsSMulRegular.{u_1, u_3} R M inst._@.Mathlib.Algebra.Regular.SMul.4090659483._hygCtx._hyg.8 b))","typeFull":"∀ {R : Type u_1} {M : Type u_3} {a b : R} [inst : SMul R M] [inst_1 : Mul R] [IsScalarTower R R M],\n IsSMulRegular M a → (IsSMulRegular M (a * b) ↔ IsSMulRegular M b)","typeReadable":"∀ {R : Type u_1} {M : Type u_3} {a b : R} [inst : SMul R M] [inst_1 : Mul R] [IsScalarTower R R M],\n IsSMulRegular M a → (IsSMulRegular M (a * b) ↔ IsSMulRegular M 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