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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GCDMonoid.FinsetLemmas.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Pointwise.Set.ListOfFn.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Action.Opposite.sym.json

@@ -0,0 +1 @@
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{α : Type.{u_3}} {β : Type.{u_4}} {R : Type.{u_5}} {M : Type.{u_6}} [inst._@.Mathlib.Algebra.Module.BigOperators.3951137540._hygCtx._hyg.8 : Semiring.{u_5} R] [inst._@.Mathlib.Algebra.Module.BigOperators.3951137540._hygCtx._hyg.11 : AddCommMonoid.{u_6} M] [inst._@.Mathlib.Algebra.Module.BigOperators.3951137540._hygCtx._hyg.14 : Module.{u_5, u_6} R M inst._@.Mathlib.Algebra.Module.BigOperators.3951137540._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Module.BigOperators.3951137540._hygCtx._hyg.11] [inst._@.Mathlib.Algebra.Module.BigOperators.3951137540._hygCtx._hyg.18 : Fintype.{u_3} α] [inst._@.Mathlib.Algebra.Module.BigOperators.3951137540._hygCtx._hyg.21 : Fintype.{u_4} β] (f : α -> R) (g : β -> M), Eq.{succ u_6} M (HSMul.hSMul.{u_5, u_6, u_6} R M M (instHSMul.{u_5, u_6} R M (SMulZeroClass.toSMul.{u_5, u_6} R M (AddZero.toZero.{u_6} M (AddZeroClass.toAddZero.{u_6} M (AddMonoid.toAddZeroClass.{u_6} M (AddCommMonoid.toAddMonoid.{u_6} M 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Notation.Pi.Defs.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Group.Units.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.sym.json

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{α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.4080304339._hygCtx._hyg.3 : AddZeroClass.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.4080304339._hygCtx._hyg.6 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.4080304339._hygCtx._hyg.9 : ExistsAddOfLE.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.4080304339._hygCtx._hyg.3)) (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.4080304339._hygCtx._hyg.6)] {a : α} {b : α} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.4080304339._hygCtx._hyg.14 : AddLeftReflectLE.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.4080304339._hygCtx._hyg.3)) (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.4080304339._hygCtx._hyg.6)], (LE.le.{u} α (Preorder.toLE.{u} α 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[inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9 : AddMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.12 : ExistsAddOfLE.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α (AddMonoid.toAddZeroClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9))) (Preorder.toLE.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3))))))] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.15 : AddLeftReflectLT.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α (AddMonoid.toAddZeroClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9))) (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3))))))] {a : α} {b : α}, (forall (ε : α), (LT.lt.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3)))))) (OfNat.ofNat.{u} α 0 (Zero.toOfNat0.{u} α (AddZero.toZero.{u} α (AddZeroClass.toAddZero.{u} α (AddMonoid.toAddZeroClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9))))) ε) -> (LT.lt.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α 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b","typeReferences":[["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["instHAdd"],["LinearOrder"],["Preorder","toLT"],["AddMonoid"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["HAdd","hAdd"],["LT","lt"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["AddLeftReflectLT"],["DenselyOrdered"],["LE","le"],["Zero","toOfNat0"],["Preorder","toLE"],["AddZero","toZero"],["ExistsAddOfLE"],["SemilatticeInf","toPartialOrder"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["HAdd","hAdd"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["instHAdd"],["le_of_forall_pos_le_add"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["AddMonoid","toAddZeroClass"],["SemilatticeInf","toPartialOrder"],["LT","lt","le"]]},{"isProp":false,"kind":"definition","name":["ExistsMulOfLE","recOn"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5 : Mul.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8 : LE.{u} α] {motive : (ExistsMulOfLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8) -> Sort.{u_1}} (t : ExistsMulOfLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8), (forall (exists_mul_of_le : forall {a : α} {b : α}, (LE.le.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8 a b) -> (Exists.{succ u} α (fun (c : α) => Eq.{succ u} α b (HMul.hMul.{u, u, u} α α α (instHMul.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5) a c)))), motive (ExistsMulOfLE.mk.{u} α 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[inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.3 : MulOneClass.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.6 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.9 : ExistsMulOfLE.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.3)) (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.6)] {a : α} {b : α} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.14 : MulLeftMono.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.3)) (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.17 : MulLeftReflectLE.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.3)) (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.6)], Iff (LE.le.{u} α (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.6) a b) (Exists.{succ u} α (fun (c : α) => And (LE.le.{u} α (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.6) (OfNat.ofNat.{u} α 1 (One.toOfNat1.{u} α (MulOne.toOne.{u} α (MulOneClass.toMulOne.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.2094765115._hygCtx._hyg.3)))) c) (Eq.{succ u} α (HMul.hMul.{u, u, u} α α α (instHMul.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α 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t","typeReferences":[["HAdd","hAdd"],["Exists"],["instHAdd"],["Add"],["ExistsAddOfLE","mk"],["LE","le"],["LE"],["Eq"],["ExistsAddOfLE"]],"valueReferences":null},{"isProp":true,"kind":"theorem","name":["exists_one_lt_mul_of_lt'"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3070282669._hygCtx._hyg.3 : MulOneClass.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3070282669._hygCtx._hyg.6 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3070282669._hygCtx._hyg.9 : ExistsMulOfLE.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3070282669._hygCtx._hyg.3)) (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3070282669._hygCtx._hyg.6)] {a : α} {b : α} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3070282669._hygCtx._hyg.14 : MulLeftReflectLT.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α 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(Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.3))))))] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.9 : Monoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.12 : ExistsMulOfLE.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.9))) (Preorder.toLE.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.3))))))] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.15 : MulLeftReflectLT.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.9))) (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.3))))))] {a : α} {b : α} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.20 : MulLeftStrictMono.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.9))) (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.3))))))], Iff (LE.le.{u} α (Preorder.toLE.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.3)))))) a b) (forall (ε : α), (LT.lt.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.3)))))) (OfNat.ofNat.{u} α 1 (One.toOfNat1.{u} α (MulOne.toOne.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.802153147._hygCtx._hyg.9))))) ε) -> (LT.lt.{u} α (Preorder.toLT.{u} α 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{α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.3 : LinearOrder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.6 : DenselyOrdered.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.3))))))] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.9 : Monoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.12 : ExistsMulOfLE.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.9))) (Preorder.toLE.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.3))))))] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.15 : MulLeftReflectLT.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.9))) (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.3))))))] {a : α} {b : α}, (forall (ε : α), (LT.lt.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.3)))))) (OfNat.ofNat.{u} α 1 (One.toOfNat1.{u} α (MulOne.toOne.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.9))))) ε) -> (LE.le.{u} α (Preorder.toLE.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.3)))))) a (HMul.hMul.{u, u, u} α α α (instHMul.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.9)))) b ε))) -> (LE.le.{u} α (Preorder.toLE.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α 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b","typeReferences":[["AddLeftMono"],["Exists"],["AddZeroClass"],["instHAdd"],["And"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["HAdd","hAdd"],["Preorder"],["Iff"],["LE","le"],["Zero","toOfNat0"],["Eq"],["Preorder","toLE"],["AddLeftReflectLE"],["AddZero","toZero"],["ExistsAddOfLE"]],"valueReferences":[["Exists"],["instHAdd"],["And"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["le_add_of_nonneg_right"],["OfNat","ofNat"],["Iff","intro"],["Exists","casesOn"],["HAdd","hAdd"],["exists_nonneg_add_of_le"],["LE","le"],["Zero","toOfNat0"],["Eq","ndrec"],["Preorder","toLE"],["Eq"],["AddZero","toZero"],["And","casesOn"]]},{"isProp":true,"kind":"definition","name":["ExistsMulOfLE","mk","_flat_ctor"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5 : Mul.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8 : LE.{u} α], (forall {a : α} {b : α}, (LE.le.{u} α 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b","typeReferences":[["Exists"],["AddZeroClass"],["instHAdd"],["Preorder","toLT"],["And"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["HAdd","hAdd"],["LT","lt"],["Preorder"],["AddLeftReflectLT"],["Zero","toOfNat0"],["Eq"],["Preorder","toLE"],["AddZero","toZero"],["ExistsAddOfLE"]],"valueReferences":[["rfl"],["Exists"],["instHAdd"],["And"],["Preorder","toLT"],["Exists","intro"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["pos_of_lt_add_right"],["OfNat","ofNat"],["Exists","casesOn"],["HAdd","hAdd"],["LT","lt"],["And","intro"],["Eq","symm"],["Zero","toOfNat0"],["Eq","ndrec"],["Preorder","toLE"],["Eq"],["AddZero","toZero"],["LT","lt","le"],["ExistsAddOfLE","exists_add_of_le"]]},{"isProp":true,"kind":"theorem","name":["lt_iff_exists_pos_add"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.3 : AddZeroClass.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.6 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.9 : ExistsAddOfLE.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.3)) (Preorder.toLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.6)] {a : α} {b : α} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.14 : AddLeftStrictMono.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.3)) (Preorder.toLT.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.17 : AddLeftReflectLT.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.3)) (Preorder.toLT.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.6)], Iff (LT.lt.{u} α (Preorder.toLT.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.6) a b) (Exists.{succ u} α (fun (c : α) => And (LT.lt.{u} α (Preorder.toLT.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.6) (OfNat.ofNat.{u} α 0 (Zero.toOfNat0.{u} α (AddZero.toZero.{u} α (AddZeroClass.toAddZero.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.3)))) c) (Eq.{succ u} α (HAdd.hAdd.{u, u, u} α α α (instHAdd.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.598359107._hygCtx._hyg.3))) a c) b)))","typeFull":"∀ {α : Type u} [inst : AddZeroClass α] [inst_1 : Preorder α] [ExistsAddOfLE α] {a b : α} [AddLeftStrictMono α]\n  [AddLeftReflectLT α], a < b ↔ ∃ c, 0 < c ∧ a + c = b","typeReadable":"∀ {α : Type u} [inst : AddZeroClass α] [inst_1 : Preorder α] [ExistsAddOfLE α] {a b : α} [AddLeftStrictMono α]\n  [AddLeftReflectLT α], a < b ↔ ∃ c, 0 < c ∧ a + c = b","typeReferences":[["Exists"],["AddZeroClass"],["instHAdd"],["AddLeftStrictMono"],["Preorder","toLT"],["And"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["HAdd","hAdd"],["LT","lt"],["Preorder"],["AddLeftReflectLT"],["Iff"],["Zero","toOfNat0"],["Eq"],["Preorder","toLE"],["AddZero","toZero"],["ExistsAddOfLE"]],"valueReferences":[["lt_add_of_pos_right"],["Exists"],["instHAdd"],["Preorder","toLT"],["And"],["exists_pos_add_of_lt'"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["OfNat","ofNat"],["Iff","intro"],["Exists","casesOn"],["LT","lt"],["HAdd","hAdd"],["Zero","toOfNat0"],["Eq","ndrec"],["Eq"],["AddZero","toZero"],["And","casesOn"]]},{"isProp":true,"kind":"theorem","name":["le_of_forall_one_lt_lt_mul'"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3 : LinearOrder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.6 : DenselyOrdered.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3))))))] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9 : Monoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.12 : ExistsMulOfLE.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9))) (Preorder.toLE.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3))))))] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.15 : MulLeftReflectLT.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9))) (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3))))))] {a : α} {b : α}, (forall (ε : α), (LT.lt.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3)))))) (OfNat.ofNat.{u} α 1 (One.toOfNat1.{u} α (MulOne.toOne.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9))))) ε) -> (LT.lt.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3)))))) a (HMul.hMul.{u, u, u} α α α (instHMul.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.9)))) b ε))) -> (LE.le.{u} α (Preorder.toLE.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.1476695857._hygCtx._hyg.3)))))) a b)","typeFull":"∀ {α : Type u} [inst : LinearOrder α] [DenselyOrdered α] [inst_2 : Monoid α] [ExistsMulOfLE α] [MulLeftReflectLT α]\n  {a b : α}, (∀ (ε : α), 1 < ε → a < b * ε) → a ≤ b","typeReadable":"∀ {α : Type u} [inst : LinearOrder α] [DenselyOrdered α] [inst_2 : Monoid α] [ExistsMulOfLE α] [MulLeftReflectLT α]\n  {a b : α}, (∀ (ε : α), 1 < ε → a < b * ε) → a ≤ b","typeReferences":[["MulOneClass","toMulOne"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["MulOne","toOne"],["LinearOrder"],["Preorder","toLT"],["HMul","hMul"],["OfNat","ofNat"],["MulLeftReflectLT"],["LT","lt"],["instDistribLatticeOfLinearOrder"],["MulOne","toMul"],["DistribLattice","toLattice"],["One","toOfNat1"],["DenselyOrdered"],["LE","le"],["Monoid","toMulOneClass"],["Monoid"],["instHMul"],["Preorder","toLE"],["ExistsMulOfLE"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["MulOneClass","toMulOne"],["instDistribLatticeOfLinearOrder"],["MulOne","toMul"],["le_of_forall_one_lt_le_mul"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["Monoid","toMulOneClass"],["instHMul"],["HMul","hMul"],["SemilatticeInf","toPartialOrder"],["LT","lt","le"]]},{"isProp":false,"kind":"definition","name":["ExistsMulOfLE","casesOn"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5 : Mul.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8 : LE.{u} α] {motive : (ExistsMulOfLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8) -> Sort.{u_1}} (t : ExistsMulOfLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8), (forall (exists_mul_of_le : forall {a : α} {b : α}, (LE.le.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8 a b) -> (Exists.{succ u} α (fun (c : α) => Eq.{succ u} α b (HMul.hMul.{u, u, u} α α α (instHMul.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5) a c)))), motive (ExistsMulOfLE.mk.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3297095689._hygCtx._hyg.8 exists_mul_of_le)) -> (motive t)","typeFull":"{α : Type u} →\n  [inst : Mul α] →\n    [inst_1 : LE α] →\n      {motive : ExistsMulOfLE α → Sort u_1} →\n        (t : ExistsMulOfLE α) → ((exists_mul_of_le : ∀ {a b : α}, a ≤ b → ∃ c, b = a * c) → motive ⋯) → motive t","typeReadable":"{α : Type u} →\n  [inst : Mul α] →\n    [inst_1 : LE α] →\n      {motive : ExistsMulOfLE α → Sort u_1} →\n        (t : ExistsMulOfLE α) → ((exists_mul_of_le : ∀ {a b : α}, a ≤ b → ∃ c, b = a * c) → motive ⋯) → motive t","typeReferences":[["Exists"],["LE","le"],["Mul"],["LE"],["instHMul"],["HMul","hMul"],["ExistsMulOfLE","mk"],["Eq"],["ExistsMulOfLE"]],"valueReferences":[["ExistsMulOfLE","rec"]]},{"isProp":true,"kind":"theorem","name":["le_of_forall_pos_le_add"],"typeFallback":"forall {α : Type.{u}} 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(DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.3))))))] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.15 : AddLeftReflectLT.{u} α (AddZero.toAdd.{u} α (AddZeroClass.toAddZero.{u} α (AddMonoid.toAddZeroClass.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.9))) (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3475583240._hygCtx._hyg.3))))))] {a : α} {b : α}, (forall (ε : α), (LT.lt.{u} α (Preorder.toLT.{u} α (PartialOrder.toPreorder.{u} α (SemilatticeInf.toPartialOrder.{u} α (Lattice.toSemilatticeInf.{u} α (DistribLattice.toLattice.{u} α (instDistribLatticeOfLinearOrder.{u} α 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{α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.5 : Add.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.8 : LE.{u} α] {motive : (ExistsAddOfLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.8) -> Sort.{u_1}} (t : ExistsAddOfLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.8), (forall (exists_add_of_le : forall {a : α} {b : α}, (LE.le.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.8 a b) -> (Exists.{succ u} α (fun (c : α) => Eq.{succ u} α b (HAdd.hAdd.{u, u, u} α α α (instHAdd.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.5) a c)))), motive (ExistsAddOfLE.mk.{u} α 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[inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.5 : Add.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.8 : LE.{u} α], (forall {a : α} {b : α}, (LE.le.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.8 a b) -> (Exists.{succ u} α (fun (c : α) => Eq.{succ u} α b (HAdd.hAdd.{u, u, u} α α α (instHAdd.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.5) a c)))) -> (ExistsAddOfLE.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE.3592962957._hygCtx._hyg.8)","typeFull":"∀ {α : Type u} [inst : Add α] [inst_1 : LE α], (∀ {a b : α}, a ≤ b → ∃ c, b = a + c) → ExistsAddOfLE α","typeReadable":"∀ {α : Type u} [inst : Add α] [inst_1 : LE α], (∀ {a b : α}, a ≤ b → ∃ c, b = a + c) → ExistsAddOfLE 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Polynomial.Eval.Algebra.sym.json

@@ -0,0 +1 @@
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{R : Type.{u}} {S : Type.{v}} [inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.14 : CommSemiring.{u} R] [inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.17 : Semiring.{v} S] [inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.20 : Algebra.{u, v} R S inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.17] (x : S) (p : Polynomial.{u} R (CommSemiring.toSemiring.{u} R inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.14)) (n : Nat), Eq.{succ v} S (Polynomial.eval₂.{u, v} R S (CommSemiring.toSemiring.{u} R inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.14) inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.17 (algebraMap.{u, v} R S inst._@.Mathlib.Algebra.Polynomial.Eval.Algebra.1369840320._hygCtx._hyg.14 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Ring.Semiconj.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Ring.Torsion.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicTopology.Quasicategory.StrictSegal.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicTopology.SimplexCategory.Rev.sym.json

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CategoryTheory.CategoryStruct.id X","typeReadable":"∀ (X : SimplexCategory),\n  SimplexCategory.Hom.mk\n      { toFun := fun i => Fin.rev ((CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.id X)) i.rev),\n        monotone' := ⋯ } =\n    CategoryTheory.CategoryStruct.id 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