Add files using upload-large-folder tool

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Finsupp.Fin.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Field.Rat.sym.json

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

@@ -0,0 +1 @@
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{α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Bounds.98788546._hygCtx._hyg.3 : AddCommGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Bounds.98788546._hygCtx._hyg.6 : LinearOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Bounds.98788546._hygCtx._hyg.9 : IsOrderedAddMonoid.{u_1} α (AddCommGroup.toAddCommMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Bounds.98788546._hygCtx._hyg.3) (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Bounds.98788546._hygCtx._hyg.6)))))] {s : Set.{u_1} α} {a : α} {ε : α}, (IsGLB.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Bounds.98788546._hygCtx._hyg.6)))))) s a) -> 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{α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Bounds.395500204._hygCtx._hyg.3 : AddCommGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Bounds.395500204._hygCtx._hyg.6 : LinearOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Bounds.395500204._hygCtx._hyg.9 : IsOrderedAddMonoid.{u_1} α (AddCommGroup.toAddCommMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Bounds.395500204._hygCtx._hyg.3) (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Bounds.395500204._hygCtx._hyg.6)))))] {s : Set.{u_1} α} {a : α} {ε : α}, (IsLUB.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Bounds.395500204._hygCtx._hyg.6)))))) s a) -> (LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Bounds.395500204._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (NegZeroClass.toZero.{u_1} α (SubNegZeroMonoid.toNegZeroClass.{u_1} α (SubtractionMonoid.toSubNegZeroMonoid.{u_1} α (SubtractionCommMonoid.toSubtractionMonoid.{u_1} α (AddCommGroup.toDivisionAddCommMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Bounds.395500204._hygCtx._hyg.3))))))) ε) -> (Exists.{succ u_1} α (fun (b : α) => And (Membership.mem.{u_1, u_1} α (Set.{u_1} α) (Set.instMembership.{u_1} α) s b) (And (LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α 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[IsOrderedAddMonoid α] {s : Set α} {a ε : α},\n  IsGLB s a → a ∉ s → 0 < ε → ∃ b ∈ s, a < b ∧ b < a + 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Group.PiLex.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"definition","name":["_private","Mathlib","Algebra","Order","Group","PiLex",0,"Pi","Lex","isOrderedCancelMonoid","match_1"],"typeFallback":"forall {ι : Type.{u_1}} {α : ι -> Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6 : LinearOrder.{u_1} ι] [inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 : forall (i : ι), PartialOrder.{u_2} (α i)] (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 : Lex.{max u_1 u_2} (forall (i : ι), α i)) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 : Lex.{max u_1 u_2} (forall (i : ι), α i)) (motive : (LT.lt.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Pi.instLTLexForall.{u_1, u_2} ι α (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) (fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a)))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58) -> Prop) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx.75.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.83 : LT.lt.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Pi.instLTLexForall.{u_1, u_2} ι α (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) (fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a)))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58), (forall (i : ι) (hi : And (forall (j : ι), ((fun (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 : ι) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 : ι) => LT.lt.{u_1} ι (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49) j i) -> (Eq.{succ u_2} (α j) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 j) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 j))) ((fun {i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64 : ι} (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) => LT.lt.{u_2} (α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) ((fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a))) i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61) i (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 i) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 i))), motive (Exists.intro.{succ u_1} ι (fun (i : ι) => And (forall (j : ι), (LT.lt.{u_1} ι (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) j i) -> (Eq.{succ u_2} (α j) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 j) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 j))) ((fun {i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64 : ι} (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) => LT.lt.{u_2} (α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) ((fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a))) i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61) i (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 i) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 i))) i hi)) -> (motive x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx.75.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.83)","typeFull":"∀ {ι : Type u_1} {α : ι → Type u_2} [inst : LinearOrder ι] [inst_1 : (i : ι) → PartialOrder (α i)]\n  (x x_1 : Lex ((i : ι) → α i)) (motive : x < x_1 → Prop) (x_2 : x < x_1),\n  (∀ (i : ι) (hi : (∀ (j : ι), (fun x1 x2 => x1 < x2) j i → x j = x_1 j) ∧ (fun {i} x1 x2 => x1 < x2) (x i) (x_1 i)),\n      motive ⋯) →\n    motive x_2","typeReadable":"∀ {ι : Type u_1} {α : ι → Type u_2} [inst : LinearOrder ι] [inst_1 : (i : ι) → PartialOrder (α i)]\n  (x x_1 : Lex ((i : ι) → α i)) (motive : x < x_1 → Prop) (x_2 : x < x_1),\n  (∀ (i : ι) (hi : (∀ (j : ι), (fun x1 x2 => x1 < x2) j i → x j = x_1 j) ∧ (fun {i} x1 x2 => x1 < x2) (x i) (x_1 i)),\n      motive ⋯) →\n    motive x_2","typeReferences":[["Pi","instLTLexForall"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["LinearOrder"],["Preorder","toLT"],["And"],["Exists","intro"],["LT","lt"],["instDistribLatticeOfLinearOrder"],["Lex"],["DistribLattice","toLattice"],["PartialOrder"],["Eq"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["LT","lt"],["Exists","casesOn"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["Preorder","toLT"],["And"],["Eq"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"definition","name":["_private","Mathlib","Algebra","Order","Group","PiLex",0,"Pi","Lex","isOrderedAddCancelMonoid","match_1"],"typeFallback":"forall {ι : Type.{u_1}} {α : ι -> Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6 : LinearOrder.{u_1} ι] [inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 : forall (i : ι), PartialOrder.{u_2} (α i)] (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 : Lex.{max u_1 u_2} (forall (i : ι), α i)) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 : Lex.{max u_1 u_2} (forall (i : ι), α i)) (motive : (LT.lt.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Pi.instLTLexForall.{u_1, u_2} ι α (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) (fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a)))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58) -> Prop) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx.75.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.83 : LT.lt.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Pi.instLTLexForall.{u_1, u_2} ι α (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) (fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a)))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58), (forall (i : ι) (hi : And (forall (j : ι), ((fun (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 : ι) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 : ι) => LT.lt.{u_1} ι (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49) j i) -> (Eq.{succ u_2} (α j) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 j) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 j))) ((fun {i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64 : ι} (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) => LT.lt.{u_2} (α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) ((fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a))) i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61) i (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 i) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 i))), motive (Exists.intro.{succ u_1} ι (fun (i : ι) => And (forall (j : ι), (LT.lt.{u_1} ι (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) j i) -> (Eq.{succ u_2} (α j) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 j) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 j))) ((fun {i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64 : ι} (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) => LT.lt.{u_2} (α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) ((fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a))) i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61) i (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.56 i) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.58 i))) i hi)) -> (motive x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx.75.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.83)","typeFull":"∀ {ι : Type u_1} {α : ι → Type u_2} [inst : LinearOrder ι] [inst_1 : (i : ι) → PartialOrder (α i)]\n  (x x_1 : Lex ((i : ι) → α i)) (motive : x < x_1 → Prop) (x_2 : x < x_1),\n  (∀ (i : ι) (hi : (∀ (j : ι), (fun x1 x2 => x1 < x2) j i → x j = x_1 j) ∧ (fun {i} x1 x2 => x1 < x2) (x i) (x_1 i)),\n      motive ⋯) →\n    motive x_2","typeReadable":"∀ {ι : Type u_1} {α : ι → Type u_2} [inst : LinearOrder ι] [inst_1 : (i : ι) → PartialOrder (α i)]\n  (x x_1 : Lex ((i : ι) → α i)) (motive : x < x_1 → Prop) (x_2 : x < x_1),\n  (∀ (i : ι) (hi : (∀ (j : ι), (fun x1 x2 => x1 < x2) j i → x j = x_1 j) ∧ (fun {i} x1 x2 => x1 < x2) (x i) (x_1 i)),\n      motive ⋯) →\n    motive x_2","typeReferences":[["Pi","instLTLexForall"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["LinearOrder"],["Preorder","toLT"],["And"],["Exists","intro"],["LT","lt"],["instDistribLatticeOfLinearOrder"],["Lex"],["DistribLattice","toLattice"],["PartialOrder"],["Eq"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["LT","lt"],["Exists","casesOn"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["Preorder","toLT"],["And"],["Eq"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"definition","name":["_private","Mathlib","Algebra","Order","Group","PiLex",0,"Pi","Lex","isOrderedCancelMonoid","match_3"],"typeFallback":"forall {ι : Type.{u_1}} {α : ι -> Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6 : LinearOrder.{u_1} ι] [inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9 : forall (i : ι), CommMonoid.{u_2} (α i)] [inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 : forall (i : ι), PartialOrder.{u_2} (α i)] (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 : Lex.{max u_1 u_2} (forall (i : ι), α i)) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129 : Lex.{max u_1 u_2} (forall (i : ι), α i)) (x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131 : Lex.{max u_1 u_2} (forall (i : ι), α i)) (motive : (LT.lt.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Pi.instLTLexForall.{u_1, u_2} ι α (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) (fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a)))) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} 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(SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) (fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a)))) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131)), (forall (i : ι) (hi : And (forall (j : ι), ((fun (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 : ι) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 : ι) => LT.lt.{u_1} ι (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49) j i) -> (Eq.{succ u_2} (α j) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129 j) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131 j))) ((fun {i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64 : ι} (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) => LT.lt.{u_2} (α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) ((fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a))) i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61) i (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129 i) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131 i))), motive (Exists.intro.{succ u_1} ι (fun (i : ι) => And (forall (j : ι), (LT.lt.{u_1} ι (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) j i) -> (Eq.{succ u_2} (α j) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129 j) (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (CommMonoid.toMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131 j))) ((fun {i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64 : ι} (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) => LT.lt.{u_2} (α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) ((fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a))) i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61) i (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOne.toMul.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (MulOneClass.toMulOne.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Monoid.toMulOneClass.{max u_1 u_2} (Lex.{max u_1 u_2} 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(Pi.commMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131 i))) i hi)) -> (motive x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx.147.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.155)","typeFull":"∀ {ι : Type u_1} {α : ι → Type u_2} [inst : LinearOrder ι] [inst_1 : (i : ι) → CommMonoid (α i)]\n  [inst_2 : (i : ι) → PartialOrder (α i)] (x x_1 x_2 : Lex ((i : ι) → α i)) (motive : x * x_1 < x * x_2 → Prop)\n  (x_3 : x * x_1 < x * x_2),\n  (∀ (i : ι)\n      (hi :\n        (∀ (j : ι), (fun x1 x2 => x1 < x2) j i → (x * x_1) j = (x * x_2) j) ∧\n          (fun {i} x1 x2 => x1 < x2) ((x * x_1) i) ((x * x_2) i)),\n      motive ⋯) →\n    motive x_3","typeReadable":"∀ {ι : Type u_1} {α : ι → Type u_2} [inst : LinearOrder ι] [inst_1 : (i : ι) → CommMonoid (α i)]\n  [inst_2 : (i : ι) → PartialOrder (α i)] (x x_1 x_2 : Lex ((i : ι) → α i)) (motive : x * x_1 < x * x_2 → Prop)\n  (x_3 : x * x_1 < x * x_2),\n  (∀ (i : ι)\n      (hi :\n        (∀ (j : ι), (fun x1 x2 => x1 < x2) j i → (x * x_1) j = (x * x_2) j) ∧\n          (fun {i} x1 x2 => x1 < x2) ((x * x_1) i) ((x * x_2) i)),\n      motive ⋯) →\n    motive 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(instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) (fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a)))) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131)) -> 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(AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131)), (forall (i : ι) (hi : And (forall (j : ι), ((fun (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 : ι) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 : ι) => LT.lt.{u_1} ι (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.49) j i) -> (Eq.{succ u_2} (α j) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129 j) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131 j))) ((fun {i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64 : ι} (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) => LT.lt.{u_2} (α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) ((fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a))) i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61) i (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129 i) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131 i))), motive (Exists.intro.{succ u_1} ι (fun (i : ι) => And (forall (j : ι), (LT.lt.{u_1} ι (Preorder.toLT.{u_1} ι (PartialOrder.toPreorder.{u_1} ι (SemilatticeInf.toPartialOrder.{u_1} ι (Lattice.toSemilatticeInf.{u_1} ι (DistribLattice.toLattice.{u_1} ι (instDistribLatticeOfLinearOrder.{u_1} ι inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.6)))))) j i) -> (Eq.{succ u_2} (α j) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129 j) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.131 j))) ((fun {i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64 : ι} (x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) (x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 : α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) => LT.lt.{u_2} (α i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) ((fun (a : ι) => Preorder.toLT.{u_2} (α a) (PartialOrder.toPreorder.{u_2} (α a) (inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.18 a))) i._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.64) x1._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61 x2._@.Mathlib.Order.PiLex.1431593913._hygCtx._hyg.61) i (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instHAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZero.toAdd.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddZeroClass.toAddZero.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddMonoid.toAddZeroClass.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (AddCommMonoid.toAddMonoid.{max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : ι), α i)) (instAddCommMonoidLex.{max u_1 u_2} (forall (i : ι), α i) (Pi.addCommMonoid.{u_1, u_2} ι α inst._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.9))))))) x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.127 x._@.Mathlib.Algebra.Order.Group.PiLex.2396638665._hygCtx._hyg.129 i) (HAdd.hAdd.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (Lex.{max u_1 u_2} (forall (i : 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Pi.sym.json

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

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Ring.Subring.IntPolynomial.sym.json

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ℕ), P.coeff n ∈ R),\n  (Polynomial.int R P hP).natDegree = P.natDegree","typeReadable":"∀ {K : Type u_1} [inst : Field K] (R : Subring K) (P : Polynomial K) (hP : ∀ (n : ℕ), P.coeff n ∈ R),\n  (Polynomial.int R P hP).natDegree = P.natDegree","typeReferences":[["Semifield","toCommSemiring"],["SubsemiringClass","toCommSemiring"],["Subtype"],["Polynomial","coeff"],["Field","toCommRing"],["SetLike","instMembership"],["Field"],["CommRing","toNonAssocCommRing"],["Subring"],["CommSemiring","toSemiring"],["Membership","mem"],["Polynomial","natDegree"],["SubringClass","toSubsemiringClass"],["Subring","instSubringClass"],["DivisionSemiring","toSemiring"],["Polynomial"],["Nat"],["Field","toSemifield"],["NonAssocCommRing","toNonAssocRing"],["Semifield","toDivisionSemiring"],["Eq"],["Polynomial","int"],["Subring","instSetLike"]],"valueReferences":[["Semifield","toCommSemiring"],["rfl"],["Subtype"],["Field","toCommRing"],["SetLike","instMembership"],["SubsemiringClass","toCommSemiring"],["CommRing","toNonAssocCommRing"],["Subring"],["Membership","mem"],["CommSemiring","toSemiring"],["Polynomial","natDegree"],["SubringClass","toSubsemiringClass"],["Subring","instSubringClass"],["Nat"],["Field","toSemifield"],["NonAssocCommRing","toNonAssocRing"],["Polynomial","int"],["Subring","instSetLike"]]},{"isProp":true,"kind":"theorem","name":["Polynomial","int_coeff_eq"],"typeFallback":"forall 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↑((Polynomial.int R P hP).coeff n) = P.coeff n","typeReferences":[["Semifield","toCommSemiring"],["SubsemiringClass","toCommSemiring"],["Subtype"],["Polynomial","coeff"],["Field","toCommRing"],["SetLike","instMembership"],["Field"],["CommRing","toNonAssocCommRing"],["Subring"],["CommSemiring","toSemiring"],["Membership","mem"],["SubringClass","toSubsemiringClass"],["Subring","instSubringClass"],["DivisionSemiring","toSemiring"],["Subtype","val"],["Polynomial"],["Nat"],["Field","toSemifield"],["NonAssocCommRing","toNonAssocRing"],["Semifield","toDivisionSemiring"],["Eq"],["Polynomial","int"],["Subring","instSetLike"]],"valueReferences":[["Semifield","toCommSemiring"],["rfl"],["Field","toCommRing"],["SetLike","instMembership"],["Polynomial","coeff"],["Subtype"],["SubsemiringClass","toCommSemiring"],["CommRing","toNonAssocCommRing"],["Subring"],["Membership","mem"],["CommSemiring","toSemiring"],["SubringClass","toSubsemiringClass"],["Subring","instSubringClass"],["Subtype","val"],["Field","toSemifield"],["NonAssocCommRing","toNonAssocRing"],["Polynomial","int"],["Subring","instSetLike"]]},{"isProp":true,"kind":"theorem","name":["Polynomial","int_eval₂_eq"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Ring.Subring.IntPolynomial.368816223._hygCtx._hyg.3 : Field.{u_1} K] (R : Subring.{u_1} K (NonAssocCommRing.toNonAssocRing.{u_1} K (CommRing.toNonAssocCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Ring.Subring.IntPolynomial.368816223._hygCtx._hyg.3)))) (P : Polynomial.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K (Field.toSemifield.{u_1} K inst._@.Mathlib.Algebra.Ring.Subring.IntPolynomial.368816223._hygCtx._hyg.3)))) (hP : forall (n : Nat), Membership.mem.{u_1, u_1} K (Subring.{u_1} K (NonAssocCommRing.toNonAssocRing.{u_1} K (CommRing.toNonAssocCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Ring.Subring.IntPolynomial.368816223._hygCtx._hyg.3)))) (SetLike.instMembership.{u_1, u_1} (Subring.{u_1} K (NonAssocCommRing.toNonAssocRing.{u_1} K (CommRing.toNonAssocCommRing.{u_1} K (Field.toCommRing.{u_1} K 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P.coeff n ∈ R),\n  (Polynomial.int R P hP).Monic ↔ P.Monic","typeReadable":"∀ {K : Type u_1} [inst : Field K] (R : Subring K) (P : Polynomial K) (hP : ∀ (n : ℕ), P.coeff n ∈ R),\n  (Polynomial.int R P hP).Monic ↔ 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Tropical.BigOperators.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["untrop_sum"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Tropical.BigOperators.750310908._hygCtx._hyg.4 : ConditionallyCompleteLinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Tropical.BigOperators.750310908._hygCtx._hyg.7 : Fintype.{u_2} S] (f : S -> (Tropical.{u_1} (WithTop.{u_1} R))), Eq.{succ u_1} (WithTop.{u_1} R) (Tropical.untrop.{u_1} (WithTop.{u_1} R) (Finset.sum.{u_2, u_1} S (Tropical.{u_1} (WithTop.{u_1} R)) (Tropical.instAddCommMonoidTropical.{u_1} (WithTop.{u_1} R) (WithTop.linearOrder.{u_1} R (ConditionallyCompleteLinearOrder.toLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Tropical.BigOperators.750310908._hygCtx._hyg.4)) (WithTop.instOrderTop.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeSup.toPartialOrder.{u_1} R (Lattice.toSemilatticeSup.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.BoxIntegral.Box.SubboxInduction.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Limits.Types.Coequalizers.sym.json

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{X : Type.{u}} {Y : Type.{u}} (f : Quiver.Hom.{u, succ u} Type.{u} (CategoryTheory.CategoryStruct.toQuiver.{u, succ u} Type.{u} (CategoryTheory.Category.toCategoryStruct.{u, succ u} Type.{u} CategoryTheory.types.{u})) X Y) (g : Quiver.Hom.{u, succ u} Type.{u} (CategoryTheory.CategoryStruct.toQuiver.{u, succ u} Type.{u} (CategoryTheory.Category.toCategoryStruct.{u, succ u} Type.{u} CategoryTheory.types.{u})) X Y), Eq.{succ u} (Quiver.Hom.{u, succ u} Type.{u} (CategoryTheory.CategoryStruct.toQuiver.{u, succ u} Type.{u} (CategoryTheory.Category.toCategoryStruct.{u, succ u} Type.{u} CategoryTheory.types.{u})) Y (Function.Coequalizer.{u, u} X Y f g)) (CategoryTheory.CategoryStruct.comp.{u, succ u} Type.{u} (CategoryTheory.Category.toCategoryStruct.{u, succ u} Type.{u} CategoryTheory.types.{u}) Y (CategoryTheory.Limits.coequalizer.{u, succ u} Type.{u} CategoryTheory.types.{u} X Y f g (CategoryTheory.Limits.Types.hasColimit.{0, u, 0} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory (UnivLE.small.{0, u} (univLE_of_max.{0, u} UnivLE.self.{u}) CategoryTheory.Limits.WalkingParallelPair) (CategoryTheory.Limits.parallelPair.{u, succ u} Type.{u} CategoryTheory.types.{u} X Y f g))) (Function.Coequalizer.{u, u} X Y f g) (CategoryTheory.Limits.coequalizer.π.{u, succ u} Type.{u} CategoryTheory.types.{u} X Y f g (CategoryTheory.Limits.Types.hasColimit.{0, u, 0} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory (UnivLE.small.{0, u} (univLE_of_max.{0, u} UnivLE.self.{u}) CategoryTheory.Limits.WalkingParallelPair) (CategoryTheory.Limits.parallelPair.{u, succ u} Type.{u} CategoryTheory.types.{u} X Y f g))) (CategoryTheory.Iso.hom.{u, succ u} Type.{u} CategoryTheory.types.{u} (CategoryTheory.Limits.coequalizer.{u, succ u} Type.{u} CategoryTheory.types.{u} X Y f g (CategoryTheory.Limits.Types.hasColimit.{0, u, 0} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory (UnivLE.small.{0, u} (univLE_of_max.{0, u} UnivLE.self.{u}) CategoryTheory.Limits.WalkingParallelPair) (CategoryTheory.Limits.parallelPair.{u, succ u} Type.{u} CategoryTheory.types.{u} X Y f g))) (Function.Coequalizer.{u, u} X Y f g) (CategoryTheory.Limits.Types.coequalizerIso.{u} X Y f g))) (Function.Coequalizer.mk.{u, u} X Y f g)","typeFull":"∀ {X Y : Type u} (f g : X ⟶ Y),\n  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coequalizer.π f g)\n      (CategoryTheory.Limits.Types.coequalizerIso f g).hom =\n    Function.Coequalizer.mk f g","typeReadable":"∀ {X Y : Type u} (f g : X ⟶ Y),\n  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coequalizer.π f g)\n      (CategoryTheory.Limits.Types.coequalizerIso f g).hom =\n    Function.Coequalizer.mk f 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