Add files using upload-large-folder tool

.gitattributes

@@ -91,3 +91,4 @@ data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.CoalgCat.
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Subobject.Comma.sym.json filter=lfs diff=lfs merge=lfs -text
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.TensorProduct.DirectLimitFG.sym.json filter=lfs diff=lfs merge=lfs -text
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Geometry.Manifold.VectorBundle.Riemannian.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.MeasureTheory.Function.SimpleFuncDenseLp.sym.json filter=lfs diff=lfs merge=lfs -text

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.FreeMonoid.UniqueProds.sym.json

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

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.LinearMap.Rat.sym.json

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

@@ -0,0 +1 @@
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[inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] (a b : α),\n  max (-a) (-b) = -min a b","typeReadable":"∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] (a b : α),\n  max (-a) (-b) = -min a 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{α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.MinMax.1960444256._hygCtx._hyg.3 : AddCommGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.MinMax.1960444256._hygCtx._hyg.6 : LinearOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.MinMax.1960444256._hygCtx._hyg.9 : IsOrderedAddMonoid.{u_1} α (AddCommGroup.toAddCommMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.MinMax.1960444256._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.MinMax.1960444256._hygCtx._hyg.6)))))] (a : α) (b : α) (c : α), LE.le.{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.MinMax.1960444256._hygCtx._hyg.6)))))) (abs.{u_1} α 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Ring.Unbundled.Rat.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Polynomial.Factors.sym.json

@@ -0,0 +1 @@
+[]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.Morphisms.FlatMono.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["AlgebraicGeometry","IsOpenImmersion","of_flat_of_mono"],"typeFallback":"forall {X : AlgebraicGeometry.Scheme.{u}} {Y : AlgebraicGeometry.Scheme.{u}} (f : Quiver.Hom.{u, succ u} AlgebraicGeometry.Scheme.{u} (CategoryTheory.CategoryStruct.toQuiver.{u, succ u} AlgebraicGeometry.Scheme.{u} (CategoryTheory.Category.toCategoryStruct.{u, succ u} AlgebraicGeometry.Scheme.{u} AlgebraicGeometry.Scheme.instCategory.{u})) X Y) [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.1647066533._hygCtx._hyg.9 : AlgebraicGeometry.Flat.{u} X Y f] [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.1647066533._hygCtx._hyg.12 : AlgebraicGeometry.LocallyOfFinitePresentation.{u} X Y f] [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.1647066533._hygCtx._hyg.15 : CategoryTheory.Mono.{u, succ u} AlgebraicGeometry.Scheme.{u} AlgebraicGeometry.Scheme.instCategory.{u} X Y f], AlgebraicGeometry.IsOpenImmersion.{u} X Y f","typeFull":"∀ {X Y : 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{X : AlgebraicGeometry.Scheme.{u}} {Y : AlgebraicGeometry.Scheme.{u}} (f : Quiver.Hom.{u, succ u} AlgebraicGeometry.Scheme.{u} (CategoryTheory.CategoryStruct.toQuiver.{u, succ u} AlgebraicGeometry.Scheme.{u} (CategoryTheory.Category.toCategoryStruct.{u, succ u} AlgebraicGeometry.Scheme.{u} AlgebraicGeometry.Scheme.instCategory.{u})) X Y) [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.3200284954._hygCtx._hyg.9 : AlgebraicGeometry.Flat.{u} X Y f] [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.3200284954._hygCtx._hyg.12 : AlgebraicGeometry.QuasiCompact.{u} X Y f] [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.3200284954._hygCtx._hyg.15 : AlgebraicGeometry.Surjective.{u} X Y f] [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.3200284954._hygCtx._hyg.18 : CategoryTheory.Mono.{u, succ u} AlgebraicGeometry.Scheme.{u} AlgebraicGeometry.Scheme.instCategory.{u} X Y f], CategoryTheory.IsIso.{u, succ u} AlgebraicGeometry.Scheme.{u} AlgebraicGeometry.Scheme.instCategory.{u} X Y f","typeFull":"∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.Flat f] [AlgebraicGeometry.QuasiCompact f]\n  [AlgebraicGeometry.Surjective f] [CategoryTheory.Mono f], CategoryTheory.IsIso f","typeReadable":"∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.Flat f] [AlgebraicGeometry.QuasiCompact f]\n  [AlgebraicGeometry.Surjective f] [CategoryTheory.Mono f], CategoryTheory.IsIso f","typeReferences":[["AlgebraicGeometry","Surjective"],["CategoryTheory","CategoryStruct","toQuiver"],["AlgebraicGeometry","Scheme","instCategory"],["Quiver","Hom"],["AlgebraicGeometry","Flat"],["CategoryTheory","IsIso"],["CategoryTheory","Mono"],["AlgebraicGeometry","Scheme"],["CategoryTheory","Category","toCategoryStruct"],["AlgebraicGeometry","QuasiCompact"]],"valueReferences":[["AlgebraicGeometry","descendsAlong_isomorphisms_surjective_inf_flat_inf_quasicompact"],["CategoryTheory","MorphismProperty","instCompleteBooleanAlgebra"],["SemilatticeInf","toMin"],["Lattice","toSemilatticeInf"],["AlgebraicGeometry","Scheme","instCategory"],["CompleteBooleanAlgebra","toCompleteLattice"],["AlgebraicGeometry","Scheme"],["CategoryTheory","Category","toCategoryStruct"],["AlgebraicGeometry","Surjective"],["And","intro"],["Min","min"],["CategoryTheory","MorphismProperty","of_pullback_fst_of_descendsAlong"],["_private","Mathlib","AlgebraicGeometry","Morphisms","FlatMono",0,"AlgebraicGeometry","Flat","isIso_of_surjective_of_mono","_proof_1_1"],["AlgebraicGeometry","Flat"],["CategoryTheory","MorphismProperty","isomorphisms"],["CategoryTheory","MorphismProperty"],["ConditionallyCompleteLattice","toLattice"],["AlgebraicGeometry","QuasiCompact"],["CompleteLattice","toConditionallyCompleteLattice"],["AlgebraicGeometry","Scheme","Pullback","instHasPullback"]]},{"isProp":true,"kind":"definition","name":["_private","Mathlib","AlgebraicGeometry","Morphisms","FlatMono",0,"AlgebraicGeometry","IsOpenImmersion","of_flat_of_mono","match_1_1"],"typeFallback":"forall {X : AlgebraicGeometry.Scheme.{u_1}} {Y : AlgebraicGeometry.Scheme.{u_1}} (f : Quiver.Hom.{u_1, succ u_1} AlgebraicGeometry.Scheme.{u_1} (CategoryTheory.CategoryStruct.toQuiver.{u_1, succ u_1} AlgebraicGeometry.Scheme.{u_1} (CategoryTheory.Category.toCategoryStruct.{u_1, succ u_1} AlgebraicGeometry.Scheme.{u_1} AlgebraicGeometry.Scheme.instCategory.{u_1})) X Y) [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.1647066533._hygCtx._hyg.9 : AlgebraicGeometry.Flat.{u_1} X Y f] [inst._@.Mathlib.AlgebraicGeometry.Morphisms.FlatMono.1647066533._hygCtx._hyg.12 : AlgebraicGeometry.LocallyOfFinitePresentation.{u_1} X Y f], let U : AlgebraicGeometry.Scheme.Opens.{u_1} Y := TopologicalSpace.Opens.mk.{u_1} (TopCat.carrier.{u_1} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, succ u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.SheafedSpace.toPresheafedSpace.{succ u_1, u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace.{u_1} (AlgebraicGeometry.Scheme.toLocallyRingedSpace.{u_1} Y))))) (AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier.{succ u_1, u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace.{u_1} (AlgebraicGeometry.Scheme.toLocallyRingedSpace.{u_1} Y))) (Set.range.{u_1, succ u_1} (TopCat.carrier.{u_1} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, succ u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.SheafedSpace.toPresheafedSpace.{succ u_1, u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace.{u_1} (AlgebraicGeometry.Scheme.toLocallyRingedSpace.{u_1} Y))))) (TopCat.carrier.{u_1} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, succ u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.SheafedSpace.toPresheafedSpace.{succ u_1, u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace.{u_1} (AlgebraicGeometry.Scheme.toLocallyRingedSpace.{u_1} X))))) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} ((fun (X : TopCat.{u_1}) (Y : TopCat.{u_1}) => ContinuousMap.{u_1, u_1} (TopCat.carrier.{u_1} X) (TopCat.carrier.{u_1} Y) (TopCat.str.{u_1} X) (TopCat.str.{u_1} Y)) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, succ u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.SheafedSpace.toPresheafedSpace.{succ u_1, u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace.{u_1} (AlgebraicGeometry.Scheme.toLocallyRingedSpace.{u_1} X)))) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, succ u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.SheafedSpace.toPresheafedSpace.{succ u_1, u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} 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(AlgebraicGeometry.PresheafedSpace.carrier.{u_1, succ u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.SheafedSpace.toPresheafedSpace.{succ u_1, u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace.{u_1} (AlgebraicGeometry.Scheme.toLocallyRingedSpace.{u_1} Y))))) ((fun (X : TopCat.{u_1}) (Y : TopCat.{u_1}) => ContinuousMap.instFunLike.{u_1, u_1} (TopCat.carrier.{u_1} X) (TopCat.carrier.{u_1} Y) (TopCat.str.{u_1} X) (TopCat.str.{u_1} Y)) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, succ u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.SheafedSpace.toPresheafedSpace.{succ u_1, u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} (AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace.{u_1} (AlgebraicGeometry.Scheme.toLocallyRingedSpace.{u_1} X)))) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, succ u_1, u_1} CommRingCat.{u_1} CommRingCat.instCategory.{u_1} 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Convex.Caratheodory.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Caratheodory","mem_convexHull_erase"],"typeFallback":"forall {𝕜 : Type.{u_1}} {E : Type.{u}} [inst._@.Mathlib.Analysis.Convex.Caratheodory.4232372624._hygCtx._hyg.4 : Field.{u_1} 𝕜] [inst._@.Mathlib.Analysis.Convex.Caratheodory.4232372624._hygCtx._hyg.7 : LinearOrder.{u_1} 𝕜] [inst._@.Mathlib.Analysis.Convex.Caratheodory.4232372624._hygCtx._hyg.10 : IsStrictOrderedRing.{u_1} 𝕜 (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.Caratheodory.4232372624._hygCtx._hyg.4))) (SemilatticeInf.toPartialOrder.{u_1} 𝕜 (Lattice.toSemilatticeInf.{u_1} 𝕜 (DistribLattice.toLattice.{u_1} 𝕜 (instDistribLatticeOfLinearOrder.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.Caratheodory.4232372624._hygCtx._hyg.7))))] [inst._@.Mathlib.Analysis.Convex.Caratheodory.4232372624._hygCtx._hyg.13 : AddCommGroup.{u} E] [inst._@.Mathlib.Analysis.Convex.Caratheodory.4232372624._hygCtx._hyg.16 : 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Normed.Field.ProperSpace.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Normed.Group.Lemmas.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.NormedSpace.Alternating.Curry.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.SpecialFunctions.Complex.Analytic.sym.json

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{f : Complex -> Complex} {x : Real}, (AnalyticAt.{0, 0, 0} Complex Complex Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) f (Complex.ofReal x)) -> (AnalyticAt.{0, 0, 0} Real Real Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real.normedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Real Real Real.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Real Real.normedAddCommGroup) 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{E : Type.{u_1}} [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853188._hygCtx._hyg.3 : NormedAddCommGroup.{u_1} E] [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853188._hygCtx._hyg.6 : NormedSpace.{0, u_1} Complex E Complex.instNormedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u_1} E inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853188._hygCtx._hyg.3)] {f : E -> Complex} {g : E -> Complex} {x : E} {s : Set.{u_1} E}, (AnalyticWithinAt.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853188._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853188._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) 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{f : Complex -> Complex} {s : Set.{0} Real} {x : Real}, (AnalyticWithinAt.{0, 0, 0} Complex Complex Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) f (Set.image.{0, 0} Real Complex Complex.ofReal s) (Complex.ofReal x)) -> (AnalyticWithinAt.{0, 0, 0} Real Real Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real.normedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Real Real Real.instRCLike 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{f : Complex -> Complex} {s : Set.{0} Real}, (AnalyticOn.{0, 0, 0} Complex Complex Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) f (Set.image.{0, 0} Real Complex Complex.ofReal s)) -> (AnalyticOn.{0, 0, 0} Real Real Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real.normedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Real Real Real.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} 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{E : Type.{u_1}} [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853189._hygCtx._hyg.3 : NormedAddCommGroup.{u_1} E] [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853189._hygCtx._hyg.6 : NormedSpace.{0, u_1} Complex E Complex.instNormedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u_1} E inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853189._hygCtx._hyg.3)] {f : E -> Complex} {g : E -> Complex} {x : E}, (AnalyticAt.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853189._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853189._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex 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{f : Complex -> Complex} {s : Set.{0} Real}, (AnalyticOn.{0, 0, 0} Complex Complex Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) f (Set.image.{0, 0} Real Complex Complex.ofReal s)) -> (AnalyticOn.{0, 0, 0} Real Real Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real.normedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Real Real Real.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} 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(Zero.toOfNat0.{0} Real Real.instZero)) x) -> (AnalyticAt.{0, 0, 0} Real Real Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real.normedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Real Real Real.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Real Real.normedAddCommGroup) (RCLike.toInnerProductSpaceReal.{0} Real Real.instRCLike)) Real.normedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Real Real Real.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Real Real.normedAddCommGroup) (RCLike.toInnerProductSpaceReal.{0} Real Real.instRCLike)) Real.log x)","typeFull":"∀ {x : ℝ}, 0 < x → AnalyticAt ℝ Real.log x","typeReadable":"∀ {x : ℝ}, 0 < x → AnalyticAt ℝ Real.log 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{f : Complex -> Complex} {s : Set.{0} Real}, (AnalyticOnNhd.{0, 0, 0} Complex Complex Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) f (Set.image.{0, 0} Real Complex Complex.ofReal s)) -> (AnalyticOnNhd.{0, 0, 0} Real Real Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real.normedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Real Real Real.instRCLike 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{E : Type.{u_1}} [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909362._hygCtx._hyg.3 : NormedAddCommGroup.{u_1} E] [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909362._hygCtx._hyg.6 : NormedSpace.{0, u_1} Complex E Complex.instNormedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u_1} E inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909362._hygCtx._hyg.3)] {f : E -> Complex} {s : Set.{u_1} E}, (AnalyticOn.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909362._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909362._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex 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→ AnalyticOn ℂ (fun z => Complex.log (f z)) s","typeReadable":"∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {s : Set E},\n  AnalyticOn ℂ f s → (∀ z ∈ s, f z ∈ Complex.slitPlane) → AnalyticOn ℂ (fun z => Complex.log (f z)) 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Type.{u_1}} [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853190._hygCtx._hyg.3 : NormedAddCommGroup.{u_1} E] [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853190._hygCtx._hyg.6 : NormedSpace.{0, u_1} Complex E Complex.instNormedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u_1} E inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853190._hygCtx._hyg.3)] {f : E -> Complex} {g : E -> Complex} {s : Set.{u_1} E}, (AnalyticOn.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853190._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853190._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} 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Real}, (AnalyticOnNhd.{0, 0, 0} Complex Complex Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) f (Set.image.{0, 0} Real Complex Complex.ofReal s)) -> (AnalyticOnNhd.{0, 0, 0} Real Real Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) Real.normedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Real Real Real.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Real Real.normedAddCommGroup) 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{E : Type.{u_1}} [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853191._hygCtx._hyg.3 : NormedAddCommGroup.{u_1} E] [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853191._hygCtx._hyg.6 : NormedSpace.{0, u_1} Complex E Complex.instNormedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u_1} E inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853191._hygCtx._hyg.3)] {f : E -> Complex} {g : E -> Complex} {s : Set.{u_1} E}, (AnalyticOnNhd.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853191._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.1659853191._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u_1} E inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909359._hygCtx._hyg.3)] {f : E -> Complex} {x : E}, (AnalyticAt.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909359._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909359._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) f x) -> (Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembership.{0} Complex) Complex.slitPlane (f x)) -> (AnalyticAt.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909359._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909359._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) (fun (z : E) => Complex.log (f z)) x)","typeFull":"∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {x : E},\n  AnalyticAt ℂ f x → f x ∈ Complex.slitPlane → AnalyticAt ℂ (fun z => Complex.log (f z)) x","typeReadable":"∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {x : E},\n  AnalyticAt ℂ f x → f x ∈ Complex.slitPlane → AnalyticAt ℂ (fun z => Complex.log (f z)) 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[inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909361._hygCtx._hyg.3 : NormedAddCommGroup.{u_1} E] [inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909361._hygCtx._hyg.6 : NormedSpace.{0, u_1} Complex E Complex.instNormedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u_1} E inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909361._hygCtx._hyg.3)] {f : E -> Complex} {s : Set.{u_1} E}, (AnalyticOnNhd.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909361._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909361._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) f s) -> (forall (z : E), (Membership.mem.{u_1, u_1} E (Set.{u_1} E) (Set.instMembership.{u_1} E) s z) -> (Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembership.{0} Complex) Complex.slitPlane (f z))) -> (AnalyticOnNhd.{0, u_1, 0} Complex E Complex (DenselyNormedField.toNontriviallyNormedField.{0} Complex Complex.instDenselyNormedField) inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909361._hygCtx._hyg.3 inst._@.Mathlib.Analysis.SpecialFunctions.Complex.Analytic.4045909361._hygCtx._hyg.6 Complex.instNormedAddCommGroup (InnerProductSpace.toNormedSpace.{0, 0} Complex Complex Complex.instRCLike (NormedAddCommGroup.toSeminormedAddCommGroup.{0} Complex Complex.instNormedAddCommGroup) (RCLike.innerProductSpace.{0} Complex Complex.instRCLike)) (fun (z : E) => Complex.log (f z)) s)","typeFull":"∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {s : Set E},\n  AnalyticOnNhd ℂ f s → (∀ z ∈ s, f z ∈ Complex.slitPlane) → AnalyticOnNhd ℂ 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.SpecialFunctions.Log.RpowTendsto.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.IsomorphismClasses.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Limits.Final.ParallelPair.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.sym.json

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+[{"isProp":true,"kind":"theorem","name":["CategoryTheory","Square","IsPullback","map"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3880878766._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] {D : Type.{u'}} [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3880878766._hygCtx._hyg.7 : CategoryTheory.Category.{v', u'} D] {sq : CategoryTheory.Square.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3880878766._hygCtx._hyg.3}, (CategoryTheory.Square.IsPullback.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3880878766._hygCtx._hyg.3 sq) -> (forall (F : CategoryTheory.Functor.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3880878766._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3880878766._hygCtx._hyg.7) [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3880878766._hygCtx._hyg.18 : 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C},\n  sq.IsPullback →\n    ∀ (F : CategoryTheory.Functor C D)\n      [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan sq.f₂₄ sq.f₃₄) F], (sq.map 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{C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] {D : Type.{u'}} [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.7 : CategoryTheory.Category.{v', u'} D] {sq : CategoryTheory.Square.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.3} (F : CategoryTheory.Functor.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.7) [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.17 : CategoryTheory.Limits.ReflectsColimit.{0, 0, v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.7 CategoryTheory.Limits.WalkingSpan 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(CategoryTheory.Square.map.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.7 sq F)) -> (CategoryTheory.Square.IsPushout.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463280._hygCtx._hyg.3 sq)","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]\n  {sq : CategoryTheory.Square C} (F : CategoryTheory.Functor C D)\n  [CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Limits.span sq.f₁₂ sq.f₁₃) F],\n  (sq.map F).IsPushout → sq.IsPushout","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]\n  {sq : CategoryTheory.Square C} (F : CategoryTheory.Functor C D)\n  [CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Limits.span sq.f₁₂ sq.f₁₃) F],\n  (sq.map F).IsPushout → sq.IsPushout","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Square","X₁"],["CategoryTheory","Square","f₁₂"],["CategoryTheory","Category"],["CategoryTheory","Limits","ReflectsColimit"],["CategoryTheory","Limits","WalkingPair"],["CategoryTheory","Limits","WidePushoutShape","category"],["CategoryTheory","Limits","span"],["CategoryTheory","Limits","WalkingSpan"],["CategoryTheory","Square"],["CategoryTheory","Square","map"],["CategoryTheory","Square","X₂"],["CategoryTheory","Square","X₃"],["CategoryTheory","Square","f₁₃"],["CategoryTheory","Square","IsPushout"]],"valueReferences":[["CategoryTheory","IsPushout","of_map"],["CategoryTheory","Square","f₂₄"],["CategoryTheory","Square","f₁₂"],["CategoryTheory","Square","X₁"],["CategoryTheory","Square","fac"],["CategoryTheory","Square","X₂"],["CategoryTheory","Square","X₃"],["CategoryTheory","Square","f₃₄"],["CategoryTheory","Square","X₄"],["CategoryTheory","Square","f₁₃"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Square","IsPullback","of_equiv"],"typeFallback":"forall 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(Equiv.{succ v, succ u} (CategoryTheory.Square.X₃.{v, succ v} Type.{v} CategoryTheory.types.{v} sq₁) (CategoryTheory.Square.X₃.{u, succ u} Type.{u} CategoryTheory.types.{u} sq₂)) (CategoryTheory.Square.X₃.{v, succ v} Type.{v} CategoryTheory.types.{v} sq₁) (CategoryTheory.Square.X₃.{u, succ u} Type.{u} CategoryTheory.types.{u} sq₂) (Equiv.instEquivLike.{succ v, succ u} (CategoryTheory.Square.X₃.{v, succ v} Type.{v} CategoryTheory.types.{v} sq₁) (CategoryTheory.Square.X₃.{u, succ u} Type.{u} CategoryTheory.types.{u} sq₂))) e₃))) -> (CategoryTheory.Square.IsPullback.{v, succ v} Type.{v} CategoryTheory.types.{v} sq₁) -> (CategoryTheory.Square.IsPullback.{u, succ u} Type.{u} CategoryTheory.types.{u} sq₂)","typeFull":"∀ {sq₁ : CategoryTheory.Square (Type v)} {sq₂ : CategoryTheory.Square (Type u)} (e₁ : sq₁.X₁ ≃ sq₂.X₁)\n  (e₂ : sq₁.X₂ ≃ sq₂.X₂) (e₃ : sq₁.X₃ ≃ sq₂.X₃) (e₄ : sq₁.X₄ ≃ sq₂.X₄),\n  ⇑e₂ ∘ sq₁.f₁₂ = sq₂.f₁₂ ∘ ⇑e₁ →\n    ⇑e₃ ∘ sq₁.f₁₃ = sq₂.f₁₃ ∘ ⇑e₁ →\n      ⇑e₄ ∘ sq₁.f₂₄ = sq₂.f₂₄ ∘ ⇑e₂ → ⇑e₄ ∘ sq₁.f₃₄ = sq₂.f₃₄ ∘ ⇑e₃ → sq₁.IsPullback → sq₂.IsPullback","typeReadable":"∀ {sq₁ : CategoryTheory.Square (Type v)} {sq₂ : CategoryTheory.Square (Type u)} (e₁ : sq₁.X₁ ≃ sq₂.X₁)\n  (e₂ : sq₁.X₂ ≃ sq₂.X₂) (e₃ : sq₁.X₃ ≃ sq₂.X₃) (e₄ : sq₁.X₄ ≃ sq₂.X₄),\n  ⇑e₂ ∘ sq₁.f₁₂ = sq₂.f₁₂ ∘ ⇑e₁ →\n    ⇑e₃ ∘ sq₁.f₁₃ = sq₂.f₁₃ ∘ ⇑e₁ →\n      ⇑e₄ ∘ sq₁.f₂₄ = sq₂.f₂₄ ∘ ⇑e₂ → ⇑e₄ ∘ sq₁.f₃₄ = sq₂.f₃₄ ∘ ⇑e₃ → sq₁.IsPullback → sq₂.IsPullback","typeReferences":[["CategoryTheory","Square","X₁"],["CategoryTheory","Square","f₁₂"],["Equiv","instEquivLike"],["CategoryTheory","types"],["Function","comp"],["CategoryTheory","Square","X₄"],["DFunLike","coe"],["Equiv"],["CategoryTheory","Square","f₂₄"],["CategoryTheory","Square"],["EquivLike","toFunLike"],["CategoryTheory","Square","X₂"],["CategoryTheory","Square","X₃"],["CategoryTheory","Square","f₃₄"],["CategoryTheory","Square","IsPullback"],["Eq"],["CategoryTheory","Square","f₁₃"]],"valueReferences":[["CategoryTheory","Square","IsPullback","iff_of_equiv"],["Iff","mp"],["CategoryTheory","types"],["CategoryTheory","Square","IsPullback"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Square","IsPushout","map_iff"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] {D : Type.{u'}} [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.7 : CategoryTheory.Category.{v', u'} D] (sq : CategoryTheory.Square.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3) (F : CategoryTheory.Functor.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.7) [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.17 : CategoryTheory.Limits.PreservesColimit.{0, 0, v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.7 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 (CategoryTheory.Square.X₁.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq) (CategoryTheory.Square.X₂.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq) (CategoryTheory.Square.X₃.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq) (CategoryTheory.Square.f₁₂.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq) (CategoryTheory.Square.f₁₃.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq)) F] [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.25 : CategoryTheory.Limits.ReflectsColimit.{0, 0, v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.7 CategoryTheory.Limits.WalkingSpan (CategoryTheory.Limits.WidePushoutShape.category.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.span.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 (CategoryTheory.Square.X₁.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq) (CategoryTheory.Square.X₂.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq) (CategoryTheory.Square.X₃.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq) (CategoryTheory.Square.f₁₂.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq) (CategoryTheory.Square.f₁₃.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.3907217900._hygCtx._hyg.3 sq)) F], Iff 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[inst_1 : CategoryTheory.Category.{v', u'} D]\n  (sq : CategoryTheory.Square C) (F : CategoryTheory.Functor C D)\n  [CategoryTheory.Limits.PreservesColimit (CategoryTheory.Limits.span sq.f₁₂ sq.f₁₃) F]\n  [CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Limits.span sq.f₁₂ sq.f₁₃) F],\n  (sq.map F).IsPushout ↔ sq.IsPushout","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Square","X₁"],["CategoryTheory","Square","f₁₂"],["CategoryTheory","Limits","ReflectsColimit"],["CategoryTheory","Category"],["CategoryTheory","Limits","WalkingPair"],["CategoryTheory","Limits","WidePushoutShape","category"],["CategoryTheory","Limits","span"],["CategoryTheory","Limits","WalkingSpan"],["CategoryTheory","Square"],["CategoryTheory","Square","map"],["Iff"],["CategoryTheory","Square","X₂"],["CategoryTheory","Square","X₃"],["CategoryTheory","Square","f₁₃"],["CategoryTheory","Square","IsPushout"],["CategoryTheory","Limits","PreservesColimit"]],"valueReferences":[["CategoryTheory","Square","map"],["CategoryTheory","Square","IsPushout","of_map"],["CategoryTheory","Square","IsPushout","map"],["CategoryTheory","Square","IsPushout"],["Iff","intro"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Square","IsPullback","map_iff"],"typeFallback":"forall {C : Type.{u}} 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sq₂.f₂₄ ∘ ⇑e₂ → ⇑e₄ ∘ sq₁.f₃₄ = sq₂.f₃₄ ∘ ⇑e₃ → (sq₁.IsPullback ↔ sq₂.IsPullback)","typeReadable":"∀ (sq₁ : CategoryTheory.Square (Type v)) (sq₂ : CategoryTheory.Square (Type u)) (e₁ : sq₁.X₁ ≃ sq₂.X₁)\n  (e₂ : sq₁.X₂ ≃ sq₂.X₂) (e₃ : sq₁.X₃ ≃ sq₂.X₃) (e₄ : sq₁.X₄ ≃ sq₂.X₄),\n  ⇑e₂ ∘ sq₁.f₁₂ = sq₂.f₁₂ ∘ ⇑e₁ →\n    ⇑e₃ ∘ sq₁.f₁₃ = sq₂.f₁₃ ∘ ⇑e₁ →\n      ⇑e₄ ∘ sq₁.f₂₄ = sq₂.f₂₄ ∘ ⇑e₂ → ⇑e₄ ∘ sq₁.f₃₄ = sq₂.f₃₄ ∘ ⇑e₃ → (sq₁.IsPullback ↔ 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{C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] {D : Type.{u'}} [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.7 : CategoryTheory.Category.{v', u'} D] {sq : CategoryTheory.Square.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.3} (F : CategoryTheory.Functor.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.7) [inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.17 : CategoryTheory.Limits.ReflectsLimit.{0, 0, v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.7 CategoryTheory.Limits.WalkingCospan 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(CategoryTheory.Square.map.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.3 D inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.7 sq F)) -> (CategoryTheory.Square.IsPullback.{v, u} C inst._@.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square.1196463279._hygCtx._hyg.3 sq)","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]\n  {sq : CategoryTheory.Square C} (F : CategoryTheory.Functor C D)\n  [CategoryTheory.Limits.ReflectsLimit (CategoryTheory.Limits.cospan sq.f₂₄ sq.f₃₄) F],\n  (sq.map F).IsPullback → sq.IsPullback","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]\n  {sq : CategoryTheory.Square C} (F : CategoryTheory.Functor C D)\n  [CategoryTheory.Limits.ReflectsLimit (CategoryTheory.Limits.cospan sq.f₂₄ sq.f₃₄) F],\n  (sq.map 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Sites.RegularEpi.sym.json

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+[{"isProp":true,"kind":"theorem","name":["_private","Mathlib","CategoryTheory","Sites","RegularEpi",0,"CategoryTheory","isRegularEpiCategory_sheaf","_simp_1_2"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty.{v, u} C (CategoryTheory.Category.toCategoryStruct.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3)) {X : CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P} {Y : CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P} {Z : CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P} (f : Quiver.Hom.{v, u} (CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P) (CategoryTheory.CategoryStruct.toQuiver.{v, u} (CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P) (CategoryTheory.Category.toCategoryStruct.{v, u} (CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P) (CategoryTheory.ObjectProperty.FullSubcategory.category.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P))) X Y) (g : Quiver.Hom.{v, u} (CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P) (CategoryTheory.CategoryStruct.toQuiver.{v, u} (CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C 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(CategoryTheory.CategoryStruct.comp.{v, u} (CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P) (CategoryTheory.Category.toCategoryStruct.{v, u} (CategoryTheory.ObjectProperty.FullSubcategory.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P) (CategoryTheory.ObjectProperty.FullSubcategory.category.{v, u} C inst._@.Mathlib.CategoryTheory.ObjectProperty.FullSubcategory.3729428301._hygCtx._hyg.3 P)) X Y Z f g))","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C)\n  {X Y Z : P.FullSubcategory} (f : X ⟶ Y) (g : Y ⟶ Z),\n  CategoryTheory.CategoryStruct.comp f.hom g.hom = (CategoryTheory.CategoryStruct.comp f g).hom","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C)\n  {X Y Z : P.FullSubcategory} (f : X ⟶ Y) (g : Y ⟶ Z),\n  CategoryTheory.CategoryStruct.comp f.hom g.hom = (CategoryTheory.CategoryStruct.comp f g).hom","typeReferences":[["CategoryTheory","ObjectProperty","FullSubcategory"],["CategoryTheory","CategoryStruct","toQuiver"],["CategoryTheory","CategoryStruct","comp"],["Quiver","Hom"],["CategoryTheory","ObjectProperty","FullSubcategory","category"],["CategoryTheory","Category"],["CategoryTheory","ObjectProperty"],["CategoryTheory","ObjectProperty","FullSubcategory","obj"],["Eq"],["CategoryTheory","InducedCategory","Hom","hom"],["CategoryTheory","Category","toCategoryStruct"]],"valueReferences":[["CategoryTheory","ObjectProperty","FullSubcategory"],["CategoryTheory","CategoryStruct","toQuiver"],["CategoryTheory","CategoryStruct","comp"],["Quiver","Hom"],["CategoryTheory","ObjectProperty","FullSubcategory","category"],["Eq","symm"],["CategoryTheory","ObjectProperty","FullSubcategory","obj"],["CategoryTheory","InducedCategory","Hom","hom"],["CategoryTheory","Category","toCategoryStruct"],["CategoryTheory","ObjectProperty","FullSubcategory","comp_hom"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","isRegularEpiCategory_sheaf"],"typeFallback":"forall {C : Type.{u_1}} {D : Type.{u_2}} [inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 : CategoryTheory.Category.{u_3, u_1} C] [inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 : CategoryTheory.Category.{u_4, u_2} D] (J : CategoryTheory.GrothendieckTopology.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) [inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.12 : CategoryTheory.Limits.HasPullbacks.{u_4, u_2} D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7] [inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.15 : CategoryTheory.Limits.HasPushouts.{u_4, u_2} D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7] [inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.18 : CategoryTheory.IsRegularEpiCategory.{u_4, u_2} D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7], 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inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7))) I (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J) G)) (fun (i : Quiver.Hom.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.CategoryStruct.toQuiver.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7))) I (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J) G)) => And (CategoryTheory.Epi.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J) F) I p) (And (CategoryTheory.Mono.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) I (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J) G) i) (Eq.{max (succ u_1) (succ u_4)} (Quiver.Hom.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.CategoryStruct.toQuiver.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7))) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J) F) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J) G)) (CategoryTheory.CategoryStruct.comp.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7)) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J) F) I (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J) G) p i) (CategoryTheory.InducedCategory.Hom.hom.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.ObjectProperty.FullSubcategory.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J)) (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J)) F G f))))))) -> (forall [inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.90 : CategoryTheory.HasSheafify.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 J D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7] [inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.94 : CategoryTheory.Balanced.{max u_1 u_4, max (max (max u_2 u_1) u_4) u_3} (CategoryTheory.Sheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 J D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.ObjectProperty.FullSubcategory.category.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Functor.category.{u_3, u_4, u_1, u_2} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_3, u_1} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4) D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.Presheaf.IsSheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7 J))], CategoryTheory.IsRegularEpiCategory.{max u_1 u_4, max (max (max u_2 u_1) u_4) u_3} (CategoryTheory.Sheaf.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.4 J D inst._@.Mathlib.CategoryTheory.Sites.RegularEpi.2802064229._hygCtx._hyg.7) (CategoryTheory.ObjectProperty.FullSubcategory.category.{max u_1 u_4, max (max 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Thin.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Combinatorics.Quiver.Cast.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Data.ENNReal.Lemmas.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Data.Int.Range.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Data.Rat.NatSqrt.Real.sym.json

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