Add files using upload-large-folder tool

.gitattributes

@@ -58,3 +58,36 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 # Video files - compressed
 *.mp4 filter=lfs diff=lfs merge=lfs -text
 *.webm filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Normed.Module.Multilinear.Curry.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Action.Basic.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.SpectralObject.Page.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.LinearAlgebra.TensorProduct.Quotient.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.Normalization.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.Limits.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Distribution.SchwartzSpace.Basic.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.FieldTheory.KummerExtension.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Calculus.FDeriv.CompCLM.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Lie.Cochain.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.Grp.Limits.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.InnerProductSpace.Coalgebra.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Comma.Over.Basic.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Bicategory.Product.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.Extension.Cotangent.LocalizationAway.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.AffineScheme.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.Kaehler.JacobiZariski.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Normed.Module.DoubleDual.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Category.Cat.Limit.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.Extension.Cotangent.BaseChange.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Sites.Hypercover.One.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Sites.Hypercover.Homotopy.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.CoalgCat.Monoidal.sym.json filter=lfs diff=lfs merge=lfs -text
+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.Algebra.Category.CoalgCat.Monoidal.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a161e8d68fa1a948a6fd5670b84a355bb3d684e5382fe7c92d99ab3a317a8623
+size 10994473

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.Grp.Limits.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:908c4c3c57e7bee2b654a5562bc304ca0d32733e35dae72cae0518a5ef557b95
+size 33262344

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:753d20365bf92390634f03ef980bfae29834703805dd62c57ff0e690051d5e40
+size 46815577

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.SpectralObject.Page.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2d71568528c1de02ab2378e20a7fd9240a214a1160261a14454ea80e7b7d9e48
+size 16781861

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Lie.Cochain.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7792fd5efe4dbb0650d4d7b0c4fa284933189b524600c229492cf3aae2b18177
+size 46393328

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.AffineScheme.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9aaece40bae641bfd653ed0227d513a69438be766ccde130967244bc49a6b5c0
+size 41204143

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.Limits.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8702236acfc01e147e0f49d5468cd60fb0dc1149d395fe5b22580770a70ab75e
+size 18414396

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.Normalization.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:773d2a3822823d7d638b79b63fcc5ecff5a62d487e6916fd387b3722f54371e6
+size 77126777

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a4aa8b1e0e6cdaece11c849f84ca24ca16feb3bd20e34e26e8f1bb7be550004c
+size 31886454

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:efb368641388d5ae0be40059ab091fed946323ed8a55cec97d05801d1daed72d
+size 12566298

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Calculus.FDeriv.CompCLM.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c4c43dfebf0762659393197efaf9d7d065b6d35a36d408663e5c14bbc46c526c
+size 14235215

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Distribution.SchwartzSpace.Basic.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:db4fbd78c1ebbd6a45d1f2ac509d9b10504fd52438edb4bdde6f69c9af656662
+size 17064499

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.InnerProductSpace.Coalgebra.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:88d552dd0e4fc69add0458eb4e75bd22b2ca9ee6725a679e8cacd8a51bcbbd65
+size 39547792

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Normed.Algebra.Ultra.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["IsUltrametricDist","of_normedAlgebra"],"typeFallback":"forall (K : Type.{u_1}) {L : Type.{u_2}} [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1034880135._hygCtx._hyg.4 : NormedField.{u_1} K] [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1034880135._hygCtx._hyg.7 : NormedDivisionRing.{u_2} L] [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1034880135._hygCtx._hyg.10 : NormedAlgebra.{u_1, u_2} K L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1034880135._hygCtx._hyg.4 (NormedRing.toSeminormedRing.{u_2} L (NormedDivisionRing.toNormedRing.{u_2} L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1034880135._hygCtx._hyg.7))] [h : IsUltrametricDist.{u_1} K (PseudoMetricSpace.toDist.{u_1} K (SeminormedRing.toPseudoMetricSpace.{u_1} K (SeminormedCommRing.toSeminormedRing.{u_1} K (NormedCommRing.toSeminormedCommRing.{u_1} K (NormedField.toNormedCommRing.{u_1} K inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1034880135._hygCtx._hyg.4)))))], IsUltrametricDist.{u_2} L (PseudoMetricSpace.toDist.{u_2} L (SeminormedRing.toPseudoMetricSpace.{u_2} L (NormedRing.toSeminormedRing.{u_2} L (NormedDivisionRing.toNormedRing.{u_2} L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1034880135._hygCtx._hyg.7))))","typeFull":"∀ (K : Type u_1) {L : Type u_2} [inst : NormedField K] [inst_1 : NormedDivisionRing L] [NormedAlgebra K L]\n  [h : IsUltrametricDist K], IsUltrametricDist L","typeReadable":"∀ (K : Type u_1) {L : Type u_2} [inst : NormedField K] [inst_1 : NormedDivisionRing L] [NormedAlgebra K L]\n  [h : IsUltrametricDist K], IsUltrametricDist L","typeReferences":[["PseudoMetricSpace","toDist"],["IsUltrametricDist"],["NormedRing","toSeminormedRing"],["NormedDivisionRing"],["SeminormedRing","toPseudoMetricSpace"],["NormedAlgebra"],["NormedField"],["NormedCommRing","toSeminormedCommRing"],["SeminormedCommRing","toSeminormedRing"],["NormedField","toNormedCommRing"],["NormedDivisionRing","toNormedRing"]],"valueReferences":[["RingHom"],["AddGroupWithOne","toAddMonoidWithOne"],["NormedAlgebra","toAlgebra"],["NormedRing","toRing"],["IsUltrametricDist"],["isUltrametricDist_iff_forall_norm_natCast_le_one"],["Semiring","toNonAssocSemiring"],["Ring","toAddGroupWithOne"],["Eq","symm"],["Eq","rec"],["NonAssocSemiring","toAddCommMonoidWithOne"],["NormedField","toNormedCommRing"],["PseudoMetricSpace","toDist"],["Real"],["Norm","norm"],["SeminormedRing","toNorm"],["DivisionSemiring","toSemiring"],["Real","instLE"],["Ring","toSemiring"],["NormedRing","toSeminormedRing"],["Nat"],["AddMonoidWithOne","toNatCast"],["id"],["Real","instOne"],["Eq","mpr"],["algebraMap"],["Semifield","toCommSemiring"],["Nat","cast"],["norm_algebraMap'"],["Eq","mp"],["RingHom","instFunLike"],["DFunLike","coe"],["congrArg"],["NormedDivisionRing","toNormedRing"],["SeminormedRing","toPseudoMetricSpace"],["NormedField","toField"],["DivisionRing","toDivisionSemiring"],["SeminormedRing","toRing"],["NormedCommRing","toNormedRing"],["NormedDivisionRing","to_normOneClass"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NormedField","toNorm"],["propext"],["Algebra","cast"],["CommSemiring","toSemiring"],["NormedDivisionRing","toNorm"],["algebraMap","coe_natCast"],["OfNat","ofNat"],["One","toOfNat1"],["LE","le"],["Field","toSemifield"],["NormedDivisionRing","toDivisionRing"],["NormedField","toNormedDivisionRing"]]},{"isProp":true,"kind":"theorem","name":["IsUltrametricDist","of_normedAlgebra'"],"typeFallback":"forall {K : Type.{u_1}} (L : Type.{u_2}) [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.4 : NormedField.{u_1} K] [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.7 : SeminormedRing.{u_2} L] [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.10 : NormOneClass.{u_2} L (SeminormedRing.toNorm.{u_2} L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.7) (AddMonoidWithOne.toOne.{u_2} L (AddGroupWithOne.toAddMonoidWithOne.{u_2} L (Ring.toAddGroupWithOne.{u_2} L (SeminormedRing.toRing.{u_2} L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.7))))] [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.13 : NormedAlgebra.{u_1, u_2} K L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.4 inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.7] [h : IsUltrametricDist.{u_2} L (PseudoMetricSpace.toDist.{u_2} L (SeminormedRing.toPseudoMetricSpace.{u_2} L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.7))], IsUltrametricDist.{u_1} K (PseudoMetricSpace.toDist.{u_1} K (SeminormedRing.toPseudoMetricSpace.{u_1} K (SeminormedCommRing.toSeminormedRing.{u_1} K (NormedCommRing.toSeminormedCommRing.{u_1} K (NormedField.toNormedCommRing.{u_1} K inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.1726914479._hygCtx._hyg.4)))))","typeFull":"∀ {K : Type u_1} (L : Type u_2) [inst : NormedField K] [inst_1 : SeminormedRing L] [NormOneClass L] [NormedAlgebra K L]\n  [h : IsUltrametricDist L], IsUltrametricDist K","typeReadable":"∀ {K : Type u_1} (L : Type u_2) [inst : NormedField K] [inst_1 : SeminormedRing L] [NormOneClass L] [NormedAlgebra K L]\n  [h : IsUltrametricDist L], IsUltrametricDist K","typeReferences":[["PseudoMetricSpace","toDist"],["SeminormedRing","toNorm"],["AddGroupWithOne","toAddMonoidWithOne"],["SeminormedCommRing","toSeminormedRing"],["SeminormedRing"],["IsUltrametricDist"],["SeminormedRing","toPseudoMetricSpace"],["Ring","toAddGroupWithOne"],["SeminormedRing","toRing"],["NormedAlgebra"],["NormedField"],["AddMonoidWithOne","toOne"],["NormedCommRing","toSeminormedCommRing"],["NormedField","toNormedCommRing"],["NormOneClass"]],"valueReferences":[["Semifield","toCommSemiring"],["RingHom"],["PartialOrder","toPreorder"],["Eq","trans"],["Eq","mp"],["dist_algebraMap'"],["RingHom","instFunLike"],["DFunLike","coe"],["NormedAlgebra","toAlgebra"],["congrArg"],["IsUltrametricDist","mk"],["SeminormedRing","toPseudoMetricSpace"],["NormedField","toField"],["Semiring","toNonAssocSemiring"],["Or"],["congr"],["SeminormedRing","toRing"],["Dist","dist"],["Preorder","toLE"],["Eq"],["NormedField","toNormedCommRing"],["SemilatticeInf","toPartialOrder"],["PseudoMetricSpace","toDist"],["Real","instMax"],["Lattice","toSemilatticeInf"],["Real"],["CommSemiring","toSemiring"],["SeminormedCommRing","toSeminormedRing"],["Ring","toSemiring"],["Real","instLE"],["le_sup_iff","_simp_3"],["Max","max"],["IsUltrametricDist","dist_triangle_max"],["LE","le"],["Field","toSemifield"],["id"],["Eq","mpr"],["NormedCommRing","toSeminormedCommRing"],["Real","linearOrder"],["algebraMap"],["LinearOrder","toLattice"]]},{"isProp":true,"kind":"theorem","name":["IsUltrametricDist","normedAlgebra_iff"],"typeFallback":"forall (K : Type.{u_1}) (L : Type.{u_2}) [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.2089562458._hygCtx._hyg.4 : NormedField.{u_1} K] [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.2089562458._hygCtx._hyg.7 : NormedDivisionRing.{u_2} L] [inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.2089562458._hygCtx._hyg.10 : NormedAlgebra.{u_1, u_2} K L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.2089562458._hygCtx._hyg.4 (NormedRing.toSeminormedRing.{u_2} L (NormedDivisionRing.toNormedRing.{u_2} L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.2089562458._hygCtx._hyg.7))], Iff (IsUltrametricDist.{u_2} L (PseudoMetricSpace.toDist.{u_2} L (SeminormedRing.toPseudoMetricSpace.{u_2} L (NormedRing.toSeminormedRing.{u_2} L (NormedDivisionRing.toNormedRing.{u_2} L inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.2089562458._hygCtx._hyg.7))))) (IsUltrametricDist.{u_1} K (PseudoMetricSpace.toDist.{u_1} K (SeminormedRing.toPseudoMetricSpace.{u_1} K (SeminormedCommRing.toSeminormedRing.{u_1} K (NormedCommRing.toSeminormedCommRing.{u_1} K (NormedField.toNormedCommRing.{u_1} K inst._@.Mathlib.Analysis.Normed.Algebra.Ultra.2089562458._hygCtx._hyg.4))))))","typeFull":"∀ (K : Type u_1) (L : Type u_2) [inst : NormedField K] [inst_1 : NormedDivisionRing L] [NormedAlgebra K L],\n  IsUltrametricDist L ↔ IsUltrametricDist K","typeReadable":"∀ (K : Type u_1) (L : Type u_2) [inst : NormedField K] [inst_1 : NormedDivisionRing L] [NormedAlgebra K L],\n  IsUltrametricDist L ↔ IsUltrametricDist K","typeReferences":[["PseudoMetricSpace","toDist"],["IsUltrametricDist"],["NormedRing","toSeminormedRing"],["NormedDivisionRing"],["SeminormedRing","toPseudoMetricSpace"],["Iff"],["NormedAlgebra"],["NormedField"],["NormedCommRing","toSeminormedCommRing"],["SeminormedCommRing","toSeminormedRing"],["NormedField","toNormedCommRing"],["NormedDivisionRing","toNormedRing"]],"valueReferences":[["NormedRing","toSeminormedRing"],["PseudoMetricSpace","toDist"],["IsUltrametricDist"],["SeminormedRing","toPseudoMetricSpace"],["IsUltrametricDist","of_normedAlgebra"],["NormedDivisionRing","to_normOneClass"],["NormedCommRing","toSeminormedCommRing"],["SeminormedCommRing","toSeminormedRing"],["NormedField","toNormedCommRing"],["IsUltrametricDist","of_normedAlgebra'"],["NormedDivisionRing","toNormedRing"],["Iff","intro"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Normed.Module.DoubleDual.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3819b77e0b72d059dd875064dccf17bee491a7053208f1f94a17db0ad46add90
+size 11978781

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Normed.Module.Multilinear.Curry.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ffbe418b4a6562e88a0d1ebb28779db4207a73311f9d8719040bb17d427d6506
+size 38058103

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Abelian.Preradical.Basic.sym.json

@@ -0,0 +1 @@
+[{"isProp":false,"kind":"definition","name":["CategoryTheory","Abelian","Preradical","ι"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] (Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3), Quiver.Hom.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3) (CategoryTheory.CategoryStruct.toQuiver.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3) (CategoryTheory.Category.toCategoryStruct.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3) (CategoryTheory.Functor.category.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3))) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3720083796._hygCtx._hyg.3)","typeFull":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] →\n    (Φ : CategoryTheory.Abelian.Preradical C) → Φ.r ⟶ CategoryTheory.Functor.id C","typeReadable":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] →\n    (Φ : CategoryTheory.Abelian.Preradical C) → Φ.r ⟶ CategoryTheory.Functor.id C","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","CategoryStruct","toQuiver"],["Quiver","Hom"],["CategoryTheory","Category"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","category"],["CategoryTheory","Category","toCategoryStruct"]],"valueReferences":[["CategoryTheory","Over"],["CategoryTheory","discreteCategory"],["CategoryTheory","Functor"],["CategoryTheory","Functor","id"],["PUnit"],["CategoryTheory","Comma","hom"],["CategoryTheory","Over","isMono"],["CategoryTheory","Functor","fromPUnit"],["CategoryTheory","Discrete"],["CategoryTheory","ObjectProperty","FullSubcategory","obj"],["CategoryTheory","Functor","category"],["CategoryTheory","instCategoryOver"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Abelian","Preradical","r_map_ι_app"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.6 : CategoryTheory.Abelian.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3] (Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3) (X : C), Eq.{succ v} (Quiver.Hom.{v, u} C (CategoryTheory.CategoryStruct.toQuiver.{v, u} C (CategoryTheory.Category.toCategoryStruct.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3)) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) X)) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3) X))) (CategoryTheory.Functor.map.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) X) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3) X) (CategoryTheory.NatTrans.app.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) X)) (CategoryTheory.NatTrans.app.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2373763427._hygCtx._hyg.3 Φ) X))","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C]\n  (Φ : CategoryTheory.Abelian.Preradical C) (X : C), Φ.r.map (Φ.ι.app X) = Φ.ι.app (Φ.r.obj X)","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C]\n  (Φ : CategoryTheory.Abelian.Preradical C) (X : C), Φ.r.map (Φ.ι.app X) = Φ.ι.app (Φ.r.obj X)","typeReferences":[["CategoryTheory","Abelian"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Category"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Category","toCategoryStruct"],["CategoryTheory","Functor","obj"],["CategoryTheory","Functor","map"],["CategoryTheory","CategoryStruct","toQuiver"],["Quiver","Hom"],["Eq"],["CategoryTheory","NatTrans","app"]],"valueReferences":[["CategoryTheory","Functor","id"],["CategoryTheory","Limits","hasFiniteWidePullbacks_of_hasFiniteLimits"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","obj"],["CategoryTheory","Limits","hasLimitsOfShape_widePullbackShape"],["Finite","of_fintype"],["congrArg"],["CategoryTheory","Functor","map"],["CategoryTheory","NatTrans","naturality"],["Quiver","Hom"],["Eq","symm"],["Eq"],["CategoryTheory","NatTrans","app"],["propext"],["CategoryTheory","Functor"],["CategoryTheory","MonoOver","mono"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Limits","WalkingPair"],["CategoryTheory","Category","toCategoryStruct"],["CategoryTheory","Limits","fintypeWalkingPair"],["CategoryTheory","CategoryStruct","toQuiver"],["CategoryTheory","Abelian","hasFiniteLimits"],["CategoryTheory","CategoryStruct","comp"],["CategoryTheory","cancel_mono"],["id"],["Eq","mpr"],["CategoryTheory","instMonoAppOfFunctor"],["CategoryTheory","Functor","category"]]},{"isProp":true,"kind":"definition","name":["CategoryTheory","Abelian","Preradical","IsIdempotent","mk","_flat_ctor"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12}, (CategoryTheory.IsIso.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.category.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ)) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12)) (CategoryTheory.Functor.whiskerLeft.{u, v, u, v, u, v} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ))) -> (CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ)","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical C},\n  CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι) → Φ.IsIdempotent","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical C},\n  CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι) → Φ.IsIdempotent","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Functor","whiskerLeft"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Functor","comp"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","category"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":[["CategoryTheory","Abelian","Preradical","IsIdempotent","mk"]]},{"isProp":false,"kind":"recursor","name":["CategoryTheory","Abelian","Preradical","IsIdempotent","rec"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12} {motive : (CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) -> Sort.{u_1}}, (forall (isIso_whiskerLeft_r_ι : CategoryTheory.IsIso.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.category.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ)) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12)) (CategoryTheory.Functor.whiskerLeft.{u, v, u, v, u, v} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ))), motive (CategoryTheory.Abelian.Preradical.IsIdempotent.mk.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ isIso_whiskerLeft_r_ι)) -> (forall (t : CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ), motive t)","typeFull":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] →\n    {Φ : CategoryTheory.Abelian.Preradical C} →\n      {motive : Φ.IsIdempotent → Sort u_1} →\n        ((isIso_whiskerLeft_r_ι : CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι)) → motive ⋯) →\n          (t : Φ.IsIdempotent) → motive t","typeReadable":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] →\n    {Φ : CategoryTheory.Abelian.Preradical C} →\n      {motive : Φ.IsIdempotent → Sort u_1} →\n        ((isIso_whiskerLeft_r_ι : CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι)) → motive ⋯) →\n          (t : Φ.IsIdempotent) → motive t","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Functor","whiskerLeft"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Abelian","Preradical","IsIdempotent","mk"],["CategoryTheory","Functor","comp"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","category"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["CategoryTheory","Abelian","Preradical","IsIdempotent","casesOn"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12} {motive : (CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) -> Sort.{u_1}} (t : CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ), (forall (isIso_whiskerLeft_r_ι : CategoryTheory.IsIso.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.category.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ)) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12)) (CategoryTheory.Functor.whiskerLeft.{u, v, u, v, u, v} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ))), motive (CategoryTheory.Abelian.Preradical.IsIdempotent.mk.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ isIso_whiskerLeft_r_ι)) -> (motive t)","typeFull":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] →\n    {Φ : CategoryTheory.Abelian.Preradical C} →\n      {motive : Φ.IsIdempotent → Sort u_1} →\n        (t : Φ.IsIdempotent) →\n          ((isIso_whiskerLeft_r_ι : CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι)) → motive ⋯) → motive t","typeReadable":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] →\n    {Φ : CategoryTheory.Abelian.Preradical C} →\n      {motive : Φ.IsIdempotent → Sort u_1} →\n        (t : Φ.IsIdempotent) →\n          ((isIso_whiskerLeft_r_ι : CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι)) → motive ⋯) → motive t","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Functor","whiskerLeft"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Abelian","Preradical","IsIdempotent","mk"],["CategoryTheory","Functor","comp"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","category"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":[["CategoryTheory","Abelian","Preradical","IsIdempotent","rec"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Abelian","Preradical","instIsIsoAppιObjROfIsIdempotent"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] (Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3) [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.11 : CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ] (X : C), CategoryTheory.IsIso.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) X)) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) X)) (CategoryTheory.NatTrans.app.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) X))","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (Φ : CategoryTheory.Abelian.Preradical C) [Φ.IsIdempotent]\n  (X : C), CategoryTheory.IsIso (Φ.ι.app (Φ.r.obj X))","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (Φ : CategoryTheory.Abelian.Preradical C) [Φ.IsIdempotent]\n  (X : C), CategoryTheory.IsIso (Φ.ι.app (Φ.r.obj X))","typeReferences":[["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","NatTrans","app"],["CategoryTheory","Functor","obj"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":[["_private","Mathlib","CategoryTheory","Abelian","Preradical","Basic",0,"CategoryTheory","Abelian","Preradical","instIsIsoAppιObjROfIsIdempotent","_proof_1"]]},{"isProp":false,"kind":"definition","name":["CategoryTheory","Abelian","Preradical","r"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.1402566731._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C], (CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.1402566731._hygCtx._hyg.3) -> (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.1402566731._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.1402566731._hygCtx._hyg.3)","typeFull":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Abelian.Preradical C → CategoryTheory.Functor C C","typeReadable":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Abelian.Preradical C → CategoryTheory.Functor C C","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Category"]],"valueReferences":[["CategoryTheory","Over"],["CategoryTheory","discreteCategory"],["CategoryTheory","Functor"],["CategoryTheory","Functor","id"],["PUnit"],["CategoryTheory","Over","isMono"],["CategoryTheory","Comma","left"],["CategoryTheory","Functor","fromPUnit"],["CategoryTheory","Discrete"],["CategoryTheory","ObjectProperty","FullSubcategory","obj"],["CategoryTheory","Functor","category"],["CategoryTheory","instCategoryOver"]]},{"isProp":false,"kind":"definition","name":["CategoryTheory","Abelian","Preradical","IsIdempotent","recOn"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12} {motive : (CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) -> Sort.{u_1}} (t : CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ), (forall (isIso_whiskerLeft_r_ι : CategoryTheory.IsIso.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.category.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ)) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12)) (CategoryTheory.Functor.whiskerLeft.{u, v, u, v, u, v} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ))), motive (CategoryTheory.Abelian.Preradical.IsIdempotent.mk.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ isIso_whiskerLeft_r_ι)) -> (motive t)","typeFull":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] →\n    {Φ : CategoryTheory.Abelian.Preradical C} →\n      {motive : Φ.IsIdempotent → Sort u_1} →\n        (t : Φ.IsIdempotent) →\n          ((isIso_whiskerLeft_r_ι : CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι)) → motive ⋯) → motive t","typeReadable":"{C : Type u} →\n  [inst : CategoryTheory.Category.{v, u} C] →\n    {Φ : CategoryTheory.Abelian.Preradical C} →\n      {motive : Φ.IsIdempotent → Sort u_1} →\n        (t : Φ.IsIdempotent) →\n          ((isIso_whiskerLeft_r_ι : CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι)) → motive ⋯) → motive t","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Functor","whiskerLeft"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Abelian","Preradical","IsIdempotent","mk"],["CategoryTheory","Functor","comp"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","category"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":[["CategoryTheory","Abelian","Preradical","IsIdempotent","rec"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Abelian","Preradical","instMonoFunctorWhiskerLeftι"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.6 : CategoryTheory.Abelian.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3] (Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3) {D : Type.{u_1}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.12 : CategoryTheory.Category.{v_1, u_1} D] (F : CategoryTheory.Functor.{v_1, v, u_1, u} D inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3), CategoryTheory.Mono.{max u_1 v, max (max (max u_1 v_1) v) u} (CategoryTheory.Functor.{v_1, v, u_1, u} D inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3) (CategoryTheory.Functor.category.{v_1, v, u_1, u} D inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3) (CategoryTheory.Functor.comp.{v_1, v, v, u_1, u, u} D inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 F (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 Φ)) (CategoryTheory.Functor.comp.{v_1, v, v, u_1, u, u} D inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 F (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3)) (CategoryTheory.Functor.whiskerLeft.{u_1, v_1, u, v, u, v} D inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 F (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2581880363._hygCtx._hyg.3 Φ))","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C]\n  (Φ : CategoryTheory.Abelian.Preradical C) {D : Type u_1} [inst_2 : CategoryTheory.Category.{v_1, u_1} D]\n  (F : CategoryTheory.Functor D C), CategoryTheory.Mono (F.whiskerLeft Φ.ι)","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C]\n  (Φ : CategoryTheory.Abelian.Preradical C) {D : Type u_1} [inst_2 : CategoryTheory.Category.{v_1, u_1} D]\n  (F : CategoryTheory.Functor D C), CategoryTheory.Mono (F.whiskerLeft Φ.ι)","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Abelian"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Functor","whiskerLeft"],["CategoryTheory","Category"],["CategoryTheory","Functor","comp"],["CategoryTheory","Mono"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","category"]],"valueReferences":[["CategoryTheory","Functor","id"],["CategoryTheory","Limits","hasFiniteWidePullbacks_of_hasFiniteLimits"],["CategoryTheory","Functor","comp"],["CategoryTheory","Mono"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","obj"],["CategoryTheory","Limits","hasLimitsOfShape_widePullbackShape"],["Finite","of_fintype"],["congrArg"],["Eq"],["CategoryTheory","NatTrans","app"],["propext"],["CategoryTheory","Functor"],["CategoryTheory","MonoOver","mono"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Limits","WalkingPair"],["CategoryTheory","Limits","fintypeWalkingPair"],["CategoryTheory","Abelian","hasFiniteLimits"],["CategoryTheory","Functor","whiskerLeft"],["id"],["inferInstance"],["Eq","mpr"],["CategoryTheory","instMonoAppOfFunctor"],["CategoryTheory","Functor","category"],["CategoryTheory","NatTrans","mono_iff_mono_app"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Abelian","Preradical","instIsIsoMapRAppιOfIsIdempotent"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.6 : CategoryTheory.Abelian.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3] (Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3) [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.11 : CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 Φ] (X : C), CategoryTheory.IsIso.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 Φ) X)) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3) X)) (CategoryTheory.Functor.map.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 Φ) X) (CategoryTheory.Functor.obj.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3) X) (CategoryTheory.NatTrans.app.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3443420740._hygCtx._hyg.3 Φ) X))","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C]\n  (Φ : CategoryTheory.Abelian.Preradical C) [Φ.IsIdempotent] (X : C), CategoryTheory.IsIso (Φ.r.map (Φ.ι.app X))","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C]\n  (Φ : CategoryTheory.Abelian.Preradical C) [Φ.IsIdempotent] (X : C), CategoryTheory.IsIso (Φ.r.map (Φ.ι.app X))","typeReferences":[["CategoryTheory","Functor","map"],["CategoryTheory","Abelian"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","NatTrans","app"],["CategoryTheory","Functor","obj"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":[["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Abelian","Preradical","instIsIsoAppιObjROfIsIdempotent"],["CategoryTheory","IsIso"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Category","toCategoryStruct"],["CategoryTheory","Functor","obj"],["congrArg"],["CategoryTheory","Functor","map"],["CategoryTheory","CategoryStruct","toQuiver"],["Quiver","Hom"],["id"],["inferInstance"],["Eq","mpr"],["CategoryTheory","Abelian","Preradical","r_map_ι_app"],["Eq"],["CategoryTheory","NatTrans","app"]]},{"isProp":false,"kind":"inductive","name":["CategoryTheory","Abelian","Preradical","IsIdempotent"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 : CategoryTheory.Category.{v, u} C], (CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) -> Prop","typeFull":"{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Abelian.Preradical C → Prop","typeReadable":"{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Abelian.Preradical C → Prop","typeReferences":[["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Category"]],"valueReferences":null},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Abelian","Preradical","IsIdempotent","isIso_whiskerLeft_r_ι"],"typeFallback":"forall {C : Type.{u}} {inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 : CategoryTheory.Category.{v, u} C} {Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12} [self : CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ], CategoryTheory.IsIso.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.category.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ)) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12)) (CategoryTheory.Functor.whiskerLeft.{u, v, u, v, u, v} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ))","typeFull":"∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {Φ : CategoryTheory.Abelian.Preradical C}\n  [self : Φ.IsIdempotent], CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι)","typeReadable":"∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {Φ : CategoryTheory.Abelian.Preradical C}\n  [self : Φ.IsIdempotent], CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι)","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Functor","whiskerLeft"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Functor","comp"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","category"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":[]},{"isProp":true,"kind":"constructor","name":["CategoryTheory","Abelian","Preradical","IsIdempotent","mk"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12}, (CategoryTheory.IsIso.{max u v, max u v} (CategoryTheory.Functor.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.category.{v, v, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ)) (CategoryTheory.Functor.comp.{v, v, v, u, u, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12)) (CategoryTheory.Functor.whiskerLeft.{u, v, u, v, u, v} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Abelian.Preradical.r.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ) (CategoryTheory.Functor.id.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12) (CategoryTheory.Abelian.Preradical.ι.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ))) -> (CategoryTheory.Abelian.Preradical.IsIdempotent.{v, u} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2879825749._hygCtx._hyg.12 Φ)","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical C},\n  CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι) → Φ.IsIdempotent","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {Φ : CategoryTheory.Abelian.Preradical C},\n  CategoryTheory.IsIso (Φ.r.whiskerLeft Φ.ι) → Φ.IsIdempotent","typeReferences":[["CategoryTheory","Functor"],["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Functor","whiskerLeft"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Functor","comp"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","Functor","category"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":null},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","CategoryTheory","Abelian","Preradical","Basic",0,"CategoryTheory","Abelian","Preradical","instIsIsoAppιObjROfIsIdempotent","_proof_1"],"typeFallback":"forall {C : Type.{u_2}} [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 : CategoryTheory.Category.{u_1, u_2} C] (Φ : CategoryTheory.Abelian.Preradical.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3) [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.11 : CategoryTheory.Abelian.Preradical.IsIdempotent.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ] (X : C), CategoryTheory.IsIso.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Functor.obj.{u_1, u_1, u_2, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{u_1, u_1, u_2, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) X)) (CategoryTheory.Functor.obj.{u_1, u_1, u_2, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Functor.id.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3) (CategoryTheory.Functor.obj.{u_1, u_1, u_2, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) X)) (CategoryTheory.NatTrans.app.{u_1, u_1, u_2, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.id.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3) (CategoryTheory.Abelian.Preradical.ι.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) (CategoryTheory.Functor.obj.{u_1, u_1, u_2, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 (CategoryTheory.Abelian.Preradical.r.{u_1, u_2} C inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.3053102874._hygCtx._hyg.3 Φ) X))","typeFull":"∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] (Φ : CategoryTheory.Abelian.Preradical C)\n  [Φ.IsIdempotent] (X : C), CategoryTheory.IsIso (Φ.ι.app (Φ.r.obj X))","typeReadable":"∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] (Φ : CategoryTheory.Abelian.Preradical C)\n  [Φ.IsIdempotent] (X : C), CategoryTheory.IsIso (Φ.ι.app (Φ.r.obj X))","typeReferences":[["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Abelian","Preradical"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","NatTrans","app"],["CategoryTheory","Functor","obj"],["CategoryTheory","Abelian","Preradical","IsIdempotent"]],"valueReferences":[["CategoryTheory","Abelian","Preradical","ι"],["CategoryTheory","Functor","id"],["CategoryTheory","Functor","whiskerLeft"],["CategoryTheory","Abelian","Preradical","IsIdempotent","isIso_whiskerLeft_r_ι"],["CategoryTheory","Functor","comp"],["CategoryTheory","Abelian","Preradical","r"],["CategoryTheory","NatIso","isIso_app_of_isIso"]]},{"isProp":false,"kind":"definition","name":["CategoryTheory","Abelian","Preradical"],"typeFallback":"forall (C : Type.{u}) [inst._@.Mathlib.CategoryTheory.Abelian.Preradical.Basic.2352066512._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C], Type.{max u v}","typeFull":"(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max u v)","typeReadable":"(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max u v)","typeReferences":[["CategoryTheory","Category"]],"valueReferences":[["CategoryTheory","Functor"],["CategoryTheory","Functor","id"],["CategoryTheory","Functor","category"],["CategoryTheory","MonoOver"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Action.Basic.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5420873783ea7a0fac392ed998f44d24b7dcb494d171e3aa2a447753fa9bf990
+size 19137174

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Bicategory.Product.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e2a8780e5d921f61d0307fee0c15a97aa2b7a8daa0b256c71cc098b07a545766
+size 23184989

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Category.Cat.Limit.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8d403dacaa0a52e666b2bb48e732d307bf05d47e9fa9a8224e6eb2d550580a5d
+size 202035557

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Comma.Over.Basic.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d79db2acc9b6693fbfed5b4239f419f6e80e020f91aa75844c97f2934f268f92
+size 23037414

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4c99220a5b88ef7988ed9ee95d5314e8255ac078d4167103d2522e4f98ede38a
+size 1467723995

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Sites.Hypercover.Homotopy.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2f3a385f05fbdaab7c63aa03375dc535232ea48af8d9ae90287b86b7a790cb33
+size 33446884

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Sites.Hypercover.One.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c8e1b398164bd27425aabf876b63d318702ead7f998d59808856082a6b3593e3
+size 58409468

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Subobject.Comma.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:953311aa6c4cef7f41cdc878e36b92148028e400be4766685417fd61b302f5cb
+size 14528825

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.FieldTheory.KummerExtension.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:26d36f30bac49a6a8192e20b2e1854d329ee1515b090174865687a71f21b3f68
+size 19930820

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e4f8536d5c45a9e22a4f1941e4a5099543ef4ad636df264a5477ee66ed368647
+size 10841779

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Geometry.Manifold.VectorBundle.Riemannian.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6154909dfee0b5b9da9ec0d2abcdedfca92b658cbebe8d070b6f995a1e391e88
+size 15301410

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.LinearAlgebra.TensorProduct.Quotient.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4605549b4c2212382ba62e1e22f80f56e74a37e4d9a7ac49046ab6f6ea98c8a8
+size 33232423

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.sym.json

@@ -0,0 +1 @@
+[{"isProp":false,"kind":"definition","name":["Submodule","Quotient","instMeasurableSpaceQuotient"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.4 : Ring.{u_1} R] [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.7 : AddCommGroup.{u_2} M] [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.10 : Module.{u_1, u_2} R M (Ring.toSemiring.{u_1} R inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.7)] {p : Submodule.{u_1, u_2} R M (Ring.toSemiring.{u_1} R inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.7) inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.10} [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.17 : MeasurableSpace.{u_2} M], MeasurableSpace.{u_2} (HasQuotient.Quotient.{u_2, u_2} M (Submodule.{u_1, u_2} R M (Ring.toSemiring.{u_1} R inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.7) inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.10) (Submodule.hasQuotient.{u_1, u_2} R M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.4 inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.7 inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.2202914794._hygCtx._hyg.10) p)","typeFull":"{R : Type u_1} →\n  {M : Type u_2} →\n    [inst : Ring R] →\n      [inst_1 : AddCommGroup M] →\n        [inst_2 : Module R M] → {p : Submodule R M} → [MeasurableSpace M] → MeasurableSpace (M ⧸ p)","typeReadable":"{R : Type u_1} →\n  {M : Type u_2} →\n    [inst : Ring R] →\n      [inst_1 : AddCommGroup M] →\n        [inst_2 : Module R M] → {p : Submodule R M} → [MeasurableSpace M] → MeasurableSpace (M ⧸ p)","typeReferences":[["Submodule","hasQuotient"],["HasQuotient","Quotient"],["Module"],["AddCommGroup","toAddCommMonoid"],["MeasurableSpace"],["AddCommGroup"],["Submodule"],["Ring","toSemiring"],["Ring"]],"valueReferences":[["Quotient","instMeasurableSpace"],["Submodule","quotientRel"]]},{"isProp":true,"kind":"theorem","name":["Submodule","Quotient","instDiscreteMeasurableSpaceQuotient"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.4 : Ring.{u_1} R] [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.7 : AddCommGroup.{u_2} M] [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.10 : Module.{u_1, u_2} R M (Ring.toSemiring.{u_1} R inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.7)] {p : Submodule.{u_1, u_2} R M (Ring.toSemiring.{u_1} R inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.7) inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.10} [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.17 : MeasurableSpace.{u_2} M] [inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.20 : DiscreteMeasurableSpace.{u_2} M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.17], DiscreteMeasurableSpace.{u_2} (HasQuotient.Quotient.{u_2, u_2} M (Submodule.{u_1, u_2} R M (Ring.toSemiring.{u_1} R inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.7) inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.10) (Submodule.hasQuotient.{u_1, u_2} R M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.4 inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.7 inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.10) p) (Submodule.Quotient.instMeasurableSpaceQuotient.{u_1, u_2} R M inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.4 inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.7 inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.10 p inst._@.Mathlib.MeasureTheory.Constructions.SubmoduleQuotient.383071636._hygCtx._hyg.17)","typeFull":"∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {p : Submodule R M}\n  [inst_3 : MeasurableSpace M] [DiscreteMeasurableSpace M], DiscreteMeasurableSpace (M ⧸ p)","typeReadable":"∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {p : Submodule R M}\n  [inst_3 : MeasurableSpace M] [DiscreteMeasurableSpace M], DiscreteMeasurableSpace (M ⧸ p)","typeReferences":[["Submodule","hasQuotient"],["DiscreteMeasurableSpace"],["Submodule","Quotient","instMeasurableSpaceQuotient"],["HasQuotient","Quotient"],["Module"],["AddCommGroup","toAddCommMonoid"],["MeasurableSpace"],["AddCommGroup"],["Submodule"],["Ring","toSemiring"],["Ring"]],"valueReferences":[["Submodule","quotientRel"],["Quotient","instDiscreteMeasurableSpace"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7098281ca15d52624b301f047a45bdfedf1d36b019d952dd4357f253587092e0
+size 10875847

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Probability.Independence.Integrable.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["MeasureTheory","MemLp","isProbabilityMeasure_of_indepFun"],"typeFallback":"forall {Ω : Type.{u_1}} {E : Type.{u_2}} {F : Type.{u_3}} [inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.5 : MeasurableSpace.{u_1} Ω] {μ : MeasureTheory.Measure.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.5} [inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.10 : NormedAddCommGroup.{u_2} E] [inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.13 : MeasurableSpace.{u_2} E] [inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.16 : OpensMeasurableSpace.{u_2} E (UniformSpace.toTopologicalSpace.{u_2} E (PseudoMetricSpace.toUniformSpace.{u_2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u_2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.10)))) inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.13] [inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.19 : MeasurableSpace.{u_3} F] (f : Ω -> E) (g : Ω -> F) {p : ENNReal}, (Ne.{1} ENNReal p (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instZeroENNReal))) -> (Ne.{1} ENNReal p (Top.top.{0} ENNReal instTopENNReal)) -> (MeasureTheory.MemLp.{u_1, u_2} Ω E inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.5 (ContinuousENorm.toENorm.{u_2} E (UniformSpace.toTopologicalSpace.{u_2} E (PseudoMetricSpace.toUniformSpace.{u_2} E (SeminormedAddGroup.toPseudoMetricSpace.{u_2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u_2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.10))))) (SeminormedAddGroup.toContinuousENorm.{u_2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u_2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.10)))) (UniformSpace.toTopologicalSpace.{u_2} E (PseudoMetricSpace.toUniformSpace.{u_2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u_2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.10)))) f p μ) -> (Not (Filter.Eventually.{u_1} Ω (fun (ω : Ω) => Eq.{succ u_2} E (f ω) (OfNat.ofNat.{u_2} E 0 (Zero.toOfNat0.{u_2} E (NegZeroClass.toZero.{u_2} E (SubNegZeroMonoid.toNegZeroClass.{u_2} E (SubtractionMonoid.toSubNegZeroMonoid.{u_2} E (SubtractionCommMonoid.toSubtractionMonoid.{u_2} E (AddCommGroup.toDivisionAddCommMonoid.{u_2} E (NormedAddCommGroup.toAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.10))))))))) (MeasureTheory.ae.{u_1, u_1} Ω (MeasureTheory.Measure.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.5) (MeasureTheory.Measure.instFunLike.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.5) (MeasureTheory.Measure.instOuterMeasureClass.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.5) μ))) -> (ProbabilityTheory.IndepFun.{u_1, u_2, u_3} Ω E F inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.5 inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.13 inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.19 f g μ) -> (MeasureTheory.IsProbabilityMeasure.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462314._hygCtx._hyg.5 μ)","typeFull":"∀ {Ω : Type u_1} {E : Type u_2} {F : Type u_3} [inst : MeasurableSpace Ω] {μ : MeasureTheory.Measure Ω}\n  [inst_1 : NormedAddCommGroup E] [inst_2 : MeasurableSpace E] [OpensMeasurableSpace E] [inst_4 : MeasurableSpace F]\n  (f : Ω → E) (g : Ω → F) {p : ENNReal},\n  p ≠ 0 →\n    p ≠ ⊤ →\n      MeasureTheory.MemLp f p μ →\n        (¬∀ᵐ (ω : Ω) ∂μ, f ω = 0) → ProbabilityTheory.IndepFun f g μ → MeasureTheory.IsProbabilityMeasure μ","typeReadable":"∀ {Ω : Type u_1} {E : Type u_2} {F : Type u_3} [inst : MeasurableSpace Ω] {μ : MeasureTheory.Measure Ω}\n  [inst_1 : NormedAddCommGroup E] [inst_2 : MeasurableSpace E] [OpensMeasurableSpace E] [inst_4 : MeasurableSpace F]\n  (f : Ω → E) (g : Ω → F) {p : ENNReal},\n  p ≠ 0 →\n    p ≠ ⊤ →\n      MeasureTheory.MemLp f p μ →\n        (¬∀ᵐ (ω : Ω) ∂μ, f ω = 0) → ProbabilityTheory.IndepFun f g μ → MeasureTheory.IsProbabilityMeasure μ","typeReferences":[["Filter","Eventually"],["SubtractionMonoid","toSubNegZeroMonoid"],["PseudoMetricSpace","toUniformSpace"],["instZeroENNReal"],["UniformSpace","toTopologicalSpace"],["MeasureTheory","IsProbabilityMeasure"],["SubtractionCommMonoid","toSubtractionMonoid"],["SeminormedAddGroup","toPseudoMetricSpace"],["NormedAddCommGroup","toAddCommGroup"],["SubNegZeroMonoid","toNegZeroClass"],["instTopENNReal"],["MeasureTheory","Measure"],["MeasureTheory","MemLp"],["NormedAddCommGroup"],["Zero","toOfNat0"],["MeasurableSpace"],["Eq"],["MeasureTheory","ae"],["SeminormedAddGroup","toContinuousENorm"],["Not"],["SeminormedAddCommGroup","toPseudoMetricSpace"],["MeasureTheory","Measure","instFunLike"],["SeminormedAddCommGroup","toSeminormedAddGroup"],["OfNat","ofNat"],["ENNReal"],["MeasureTheory","Measure","instOuterMeasureClass"],["ContinuousENorm","toENorm"],["AddCommGroup","toDivisionAddCommMonoid"],["Top","top"],["NegZeroClass","toZero"],["ProbabilityTheory","IndepFun"],["Ne"],["NormedAddCommGroup","toSeminormedAddCommGroup"],["OpensMeasurableSpace"]],"valueReferences":[["implies_congr"],["SubtractionMonoid","toSubNegZeroMonoid"],["not_lt","_simp_1"],["PseudoMetricSpace","toUniformSpace"],["Eq","trans"],["instZeroENNReal"],["instClosedIciTopology"],["MeasureTheory","IsProbabilityMeasure"],["instENormedAddCommMonoidENNReal"],["MeasureTheory","ae_all_iff"],["Filter","univ_mem'"],["AddGroup","toSubtractionMonoid"],["ENNReal","instLinearOrder"],["NNReal","instLinearOrder"],["NNReal","instCanonicallyOrderedAdd"],["Eq","symm"],["ge_of_tendsto'"],["NonAssocSemiring","toAddCommMonoidWithOne"],["nhds"],["Set","instInter"],["Exists"],["ProbabilityTheory","IndepFun","measure_inter_preimage_eq_mul"],["NNReal"],["TopologicalSpace","PseudoMetrizableSpace","firstCountableTopology"],["MeasureTheory","Measure","instFunLike"],["instCountableNat"],["Set","instMembership"],["MeasurableSet","univ"],["Filter","atTop"],["OrderTopology","to_orderClosedTopology"],["instNonemptyOfInhabited"],["Eq","refl"],["NormedAddCommGroup","toNormedAddGroup"],["AddMonoidWithOne","toOne"],["Top","top"],["MeasureTheory","MemLp","meas_ge_lt_top"],["instInhabitedNat"],["Mathlib","Tactic","Push","not_and_eq"],["Eq","mpr"],["ENNReal","instTopologicalSpace"],["setOf"],["AddMonoid","toAddZeroClass"],["ESeminormedAddCommMonoid","toESeminormedAddMonoid"],["ENNReal","instCanonicallyOrderedAdd"],["SubtractionCommMonoid","toSubtractionMonoid"],["continuous_nnnorm"],["Nat","instPreorder"],["NNReal","instIsStrictOrderedRing"],["LT","lt","ne'"],["Nat","instSemiring"],["NormedAddGroup","toAddGroup"],["instMetricSpaceNNReal"],["Eq"],["Preorder","toLE"],["MeasureTheory","ae"],["ESeminormedAddMonoid","toAddMonoid"],["isClosed_le"],["IsStrictOrderedRing","toIsOrderedRing"],["Set"],["Filter","atTop_neBot"],["SeminormedAddCommGroup","toSeminormedAddGroup"],["OfNat","ofNat"],["Set","univ"],["SeminormedAddGroup","toNNNorm"],["LinearOrder","toPartialOrder"],["ENNReal"],["AddCommGroup","toDivisionAddCommMonoid"],["exists_seq_strictAnti_tendsto"],["nnnorm_eq_zero","_simp_1"],["IsStrictOrderedRing","toNoMaxOrder"],["Nat","instIsStrictOrderedRing"],["EMetricSpace","toPseudoEMetricSpace"],["And","casesOn"],["Filter","Eventually"],["NNReal","instTopologicalSpace"],["PartialOrder","toPreorder"],["Inter","inter"],["Membership","mem"],["Iff","mp"],["Preorder","toLT"],["HMul","hMul"],["instAddCommMonoidWithOneENNReal"],["AddMonoidWithOne","toAddMonoid"],["NormedAddCommGroup","toAddCommGroup"],["NNNorm","nnnorm"],["NNReal","instZero"],["Semiring","toNonAssocSemiring"],["LT","lt","ne"],["forall_congr"],["funext"],["Filter","Tendsto"],["Set","inter_univ"],["nonpos_iff_eq_zero","_simp_1"],["binderNameHint"],["NonUnitalNonAssocSemiring","toDistrib"],["Nat","instPartialOrder"],["Mathlib","Tactic","Contrapose","contrapose₂"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["And"],["AddZeroClass","toAddZero"],["Exists","casesOn"],["Nat"],["PseudoEMetricSpace","pseudoMetrizableSpace"],["NNReal","instOrderTopology"],["Iff","mpr"],["id"],["NegZeroClass","toZero"],["ENormedAddCommMonoid","toESeminormedAddCommMonoid"],["instHMul"],["instArchimedeanNat"],["ENNReal","instPartialOrder"],["AddZero","toZero"],["Eq","mp"],["Filter","mp_mem"],["UniformSpace","toTopologicalSpace"],["instIsDirectedOrder"],["NNReal","instPartialOrder"],["SeminormedAddGroup","toPseudoMetricSpace"],["SubNegZeroMonoid","toNegZeroClass"],["DFunLike","coe"],["instTopENNReal"],["congrArg"],["Mathlib","Tactic","Push","not_exists","_simp_1"],["MeasureTheory","Measure"],["continuous_const"],["Zero","toOfNat0"],["congrFun'"],["MetricSpace","toEMetricSpace"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["LT","lt","le"],["Not"],["IsClosed","measurableSet"],["Set","preimage"],["CommSemiring","toSemiring"],["Distrib","toMul"],["ENNReal","mul_eq_left"],["ENNReal","instCommSemiring"],["MeasureTheory","IsProbabilityMeasure","mk"],["LT","lt"],["StrictAnti"],["MeasureTheory","Measure","instOuterMeasureClass"],["One","toOfNat1"],["LE","le"],["NNReal","instSemiring"],["NormedAddCommGroup","toSeminormedAddCommGroup"],["_private","Mathlib","Probability","Independence","Integrable",0,"MeasureTheory","MemLp","isProbabilityMeasure_of_indepFun","_simp_1_1"],["NNReal","instDenselyOrdered"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Probability","Independence","Integrable",0,"MeasureTheory","MemLp","isProbabilityMeasure_of_indepFun","_simp_1_1"],"typeFallback":"forall {α : Type.{u_1}} {F : Type.{u_3}} [inst._@.Mathlib.MeasureTheory.OuterMeasure.AE.3787073176._hygCtx._hyg.5 : FunLike.{succ u_3, succ u_1, 1} F (Set.{u_1} α) ENNReal] [inst._@.Mathlib.MeasureTheory.OuterMeasure.AE.3787073176._hygCtx._hyg.15 : MeasureTheory.OuterMeasureClass.{u_3, u_1} F α inst._@.Mathlib.MeasureTheory.OuterMeasure.AE.3787073176._hygCtx._hyg.5] {μ : F} {p : α -> Prop}, Eq.{1} Prop (Filter.Eventually.{u_1} α (fun (a : α) => p a) (MeasureTheory.ae.{u_1, u_3} α F inst._@.Mathlib.MeasureTheory.OuterMeasure.AE.3787073176._hygCtx._hyg.5 inst._@.Mathlib.MeasureTheory.OuterMeasure.AE.3787073176._hygCtx._hyg.15 μ)) (Eq.{1} ENNReal (DFunLike.coe.{succ u_3, succ u_1, 1} F (Set.{u_1} α) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Set.{u_1} α) => ENNReal) inst._@.Mathlib.MeasureTheory.OuterMeasure.AE.3787073176._hygCtx._hyg.5 μ (setOf.{u_1} α (fun (a : α) => Not (p a)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instZeroENNReal)))","typeFull":"∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]\n  {μ : F} {p : α → Prop}, (∀ᵐ (a : α) ∂μ, p a) = (μ {a | ¬p a} = 0)","typeReadable":"∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]\n  {μ : F} {p : α → Prop}, (∀ᵐ (a : α) ∂μ, p a) = (μ {a | ¬p a} = 0)","typeReferences":[["Filter","Eventually"],["Not"],["FunLike"],["Set"],["instZeroENNReal"],["DFunLike","coe"],["OfNat","ofNat"],["ENNReal"],["MeasureTheory","OuterMeasureClass"],["Zero","toOfNat0"],["Eq"],["MeasureTheory","ae"],["setOf"]],"valueReferences":[["Filter","Eventually"],["Not"],["MeasureTheory","ae_iff"],["Set"],["instZeroENNReal"],["DFunLike","coe"],["OfNat","ofNat"],["ENNReal"],["Zero","toOfNat0"],["Eq"],["MeasureTheory","ae"],["propext"],["setOf"]]},{"isProp":true,"kind":"theorem","name":["MeasureTheory","Integrable","isProbabilityMeasure_of_indepFun"],"typeFallback":"forall {Ω : Type.{u_1}} {E : Type.{u_2}} {F : Type.{u_3}} [inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.5 : MeasurableSpace.{u_1} Ω] {μ : MeasureTheory.Measure.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.5} [inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.10 : NormedAddCommGroup.{u_2} E] [inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.13 : MeasurableSpace.{u_2} E] [inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.16 : OpensMeasurableSpace.{u_2} E (UniformSpace.toTopologicalSpace.{u_2} E (PseudoMetricSpace.toUniformSpace.{u_2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u_2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.10)))) inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.13] [inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.19 : MeasurableSpace.{u_3} F] (f : Ω -> E) (g : Ω -> F), (MeasureTheory.Integrable.{u_2, u_1} E (UniformSpace.toTopologicalSpace.{u_2} E (PseudoMetricSpace.toUniformSpace.{u_2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u_2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.10)))) (SeminormedAddGroup.toContinuousENorm.{u_2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u_2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.10))) Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.5 f μ) -> (Not (Filter.Eventually.{u_1} Ω (fun (ω : Ω) => Eq.{succ u_2} E (f ω) (OfNat.ofNat.{u_2} E 0 (Zero.toOfNat0.{u_2} E (NegZeroClass.toZero.{u_2} E (SubNegZeroMonoid.toNegZeroClass.{u_2} E (SubtractionMonoid.toSubNegZeroMonoid.{u_2} E (SubtractionCommMonoid.toSubtractionMonoid.{u_2} E (AddCommGroup.toDivisionAddCommMonoid.{u_2} E (NormedAddCommGroup.toAddCommGroup.{u_2} E inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.10))))))))) (MeasureTheory.ae.{u_1, u_1} Ω (MeasureTheory.Measure.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.5) (MeasureTheory.Measure.instFunLike.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.5) (MeasureTheory.Measure.instOuterMeasureClass.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.5) μ))) -> (ProbabilityTheory.IndepFun.{u_1, u_2, u_3} Ω E F inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.5 inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.13 inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.19 f g μ) -> (MeasureTheory.IsProbabilityMeasure.{u_1} Ω inst._@.Mathlib.Probability.Independence.Integrable.3458462315._hygCtx._hyg.5 μ)","typeFull":"∀ {Ω : Type u_1} {E : Type u_2} {F : Type u_3} [inst : MeasurableSpace Ω] {μ : MeasureTheory.Measure Ω}\n  [inst_1 : NormedAddCommGroup E] [inst_2 : MeasurableSpace E] [OpensMeasurableSpace E] [inst_4 : MeasurableSpace F]\n  (f : Ω → E) (g : Ω → F),\n  MeasureTheory.Integrable f μ →\n    (¬∀ᵐ (ω : Ω) ∂μ, f ω = 0) → ProbabilityTheory.IndepFun f g μ → MeasureTheory.IsProbabilityMeasure μ","typeReadable":"∀ {Ω : Type u_1} {E : Type u_2} {F : Type u_3} [inst : MeasurableSpace Ω] {μ : MeasureTheory.Measure Ω}\n  [inst_1 : NormedAddCommGroup E] [inst_2 : MeasurableSpace E] [OpensMeasurableSpace E] [inst_4 : MeasurableSpace F]\n  (f : Ω → E) (g : Ω → F),\n  MeasureTheory.Integrable f μ →\n    (¬∀ᵐ (ω : Ω) ∂μ, f ω = 0) → ProbabilityTheory.IndepFun f g μ → MeasureTheory.IsProbabilityMeasure μ","typeReferences":[["Filter","Eventually"],["SubtractionMonoid","toSubNegZeroMonoid"],["PseudoMetricSpace","toUniformSpace"],["UniformSpace","toTopologicalSpace"],["MeasureTheory","IsProbabilityMeasure"],["SubtractionCommMonoid","toSubtractionMonoid"],["SubNegZeroMonoid","toNegZeroClass"],["NormedAddCommGroup","toAddCommGroup"],["MeasureTheory","Measure"],["NormedAddCommGroup"],["MeasurableSpace"],["Zero","toOfNat0"],["Eq"],["MeasureTheory","ae"],["MeasureTheory","Integrable"],["SeminormedAddGroup","toContinuousENorm"],["Not"],["SeminormedAddCommGroup","toPseudoMetricSpace"],["SeminormedAddCommGroup","toSeminormedAddGroup"],["MeasureTheory","Measure","instFunLike"],["OfNat","ofNat"],["MeasureTheory","Measure","instOuterMeasureClass"],["AddCommGroup","toDivisionAddCommMonoid"],["NegZeroClass","toZero"],["ProbabilityTheory","IndepFun"],["NormedAddCommGroup","toSeminormedAddCommGroup"],["OpensMeasurableSpace"]],"valueReferences":[["ENNReal","one_ne_top"],["MeasureTheory","memLp_one_iff_integrable"],["PseudoMetricSpace","toUniformSpace"],["instZeroENNReal"],["SeminormedAddCommGroup","toPseudoMetricSpace"],["UniformSpace","toTopologicalSpace"],["instAddCommMonoidWithOneENNReal"],["one_ne_zero"],["ENNReal","instCharZero"],["SeminormedAddCommGroup","toSeminormedAddGroup"],["OfNat","ofNat"],["ENNReal"],["ContinuousENorm","toENorm"],["MeasureTheory","MemLp","isProbabilityMeasure_of_indepFun"],["One","toOfNat1"],["MeasureTheory","MemLp"],["Iff","mpr"],["AddMonoidWithOne","toOne"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NeZero","charZero_one"],["NormedAddCommGroup","toSeminormedAddCommGroup"],["MeasureTheory","Integrable"],["SeminormedAddGroup","toContinuousENorm"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:218be475117f5b6a1e1289afbfe8e682dd7fdea2437b0ee6b6cc33c2097fabba
+size 36486233

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.Extension.Cotangent.BaseChange.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ea7e50038004fe950d7ddf916227e936427bf60c7b6813aec035eb11af50a69a
+size 26679319

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.Extension.Cotangent.LocalizationAway.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1032da97788f0b60f000a015b20a1412878d13445c305c9ca0b61adfe0efc0fa
+size 29910130

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.Kaehler.JacobiZariski.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:72b64b195c26a6ececee01f0c54c8e2719627c2a5911445340e810afb74fc2d6
+size 20395054

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.PowerSeries.Binomial.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["PowerSeries","binomialSeries_zero"],"typeFallback":"forall {R : Type.{u_1}} {A : Type.{u_2}} [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.4 : CommRing.{u_1} R] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.7 : BinomialRing.{u_1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} R (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} R (CommRing.toNonUnitalCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.4))))) (Monoid.toPow.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.4)))))] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.10 : Ring.{u_2} A] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.13 : Algebra.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.10)], Eq.{succ u_2} (PowerSeries.{u_2} A) (PowerSeries.binomialSeries.{u_1, u_2} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.4 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.7 A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.10))) (Algebra.toSMul.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.10) inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.13) (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (MulZeroClass.toZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} R (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} R (CommRing.toNonUnitalCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.4))))))))) (OfNat.ofNat.{u_2} (PowerSeries.{u_2} A) 1 (One.toOfNat1.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instOne.{0, u_2} Unit A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.625638370._hygCtx._hyg.10))))","typeFull":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Ring A] [inst_3 : Algebra R A],\n  PowerSeries.binomialSeries A 0 = 1","typeReadable":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Ring A] [inst_3 : Algebra R A],\n  PowerSeries.binomialSeries A 0 = 1","typeReferences":[["AddGroupWithOne","toAddMonoidWithOne"],["CommRing","toNonUnitalCommRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Monoid","toPow"],["Ring","toAddGroupWithOne"],["MvPowerSeries","instOne"],["MonoidWithZero","toMonoid"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Algebra","toSMul"],["Zero","toOfNat0"],["Eq"],["PowerSeries","binomialSeries"],["PowerSeries"],["CommRing","toCommSemiring"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["CommRing"],["OfNat","ofNat"],["Unit"],["Algebra"],["Ring","toSemiring"],["One","toOfNat1"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["AddMonoidWithOne","toOne"],["Ring"],["BinomialRing"]],"valueReferences":[["MulOneClass","toMulOne"],["PowerSeries","X"],["Ring","toNonAssocRing"],["Nat","cast"],["Eq","mp"],["AddGroupWithOne","toAddMonoidWithOne"],["AddMonoidWithOne","toAddMonoid"],["PowerSeries","binomialSeries_nat"],["MvPowerSeries","instRing"],["congrArg"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["Monoid","toPow"],["instOfNatNat"],["congr"],["Monoid","toMulOneClass"],["MvPowerSeries","instOne"],["Algebra","toSMul"],["MonoidWithZero","toMonoid"],["Zero","toOfNat0"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["PowerSeries","binomialSeries"],["instHPow"],["PowerSeries"],["Distrib","toAdd"],["CommRing","toCommSemiring"],["MvPowerSeries","instSemiring"],["MulOne","toOne"],["NonUnitalNonAssocSemiring","toDistrib"],["instHAdd"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["HPow","hPow"],["OfNat","ofNat"],["Ring","toSemiring"],["Unit"],["HAdd","hAdd"],["CommRing","toRing"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["Nat","cast_zero"],["AddMonoidWithOne","toOne"],["pow_zero"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","RingTheory","PowerSeries","Binomial",0,"PowerSeries","rescale_neg_one_invOneSubPow","_proof_1_1"],"typeFallback":"forall (n : Nat) (d : Nat), Eq.{1} Int (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSub) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAdd) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAdd) (NatCast.natCast.{0} Int instNatCastInt d) (OfNat.ofNat.{0} Int 1 (instOfNat 1))) (NatCast.natCast.{0} Int instNatCastInt n)) (OfNat.ofNat.{0} Int 1 (instOfNat 1))) (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAdd) (NatCast.natCast.{0} Int instNatCastInt d) (NatCast.natCast.{0} Int instNatCastInt n))","typeFull":"∀ (n d : ℕ), ↑d + 1 + ↑n - 1 = ↑d + ↑n","typeReadable":"∀ (n d : ℕ), ↑d + 1 + ↑n - 1 = ↑d + ↑n","typeReferences":[["Int","instSub"],["instHAdd"],["OfNat","ofNat"],["Int"],["HAdd","hAdd"],["Nat"],["instOfNat"],["NatCast","natCast"],["Int","instAdd"],["HSub","hSub"],["Eq"],["instHSub"],["instNatCastInt"]],"valueReferences":[["Lean","Grind","not_true"],["Int","instSub"],["Bool"],["Eq","trans"],["eagerReduce"],["Int","Linear","Expr","var"],["congrArg"],["Lean","RArray","leaf"],["instOfNatNat"],["NatCast","natCast"],["False","casesOn"],["Int","instAdd"],["HSub","hSub"],["Lean","RArray","branch"],["Eq"],["Int","Linear","eq_eq_true"],["Bool","true"],["instNatCastInt"],["Not"],["True"],["instHAdd"],["Int","Linear","Expr","sub"],["Int","Linear","Expr","add"],["Int","Linear","Expr","num"],["OfNat","ofNat"],["Int"],["HAdd","hAdd"],["Nat"],["instOfNat"],["Eq","refl"],["Classical","byContradiction"],["id"],["False"],["Lean","Grind","intro_with_eq"],["instHSub"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","RingTheory","PowerSeries","Binomial",0,"PowerSeries","binomialSeries_constantCoeff","_simp_1_1"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3 : Semiring.{u_1} R] (φ : PowerSeries.{u_1} R), Eq.{succ u_1} R (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (RingHom.{u_1, u_1} (PowerSeries.{u_1} R) R (Semiring.toNonAssocSemiring.{u_1} (PowerSeries.{u_1} R) (MvPowerSeries.instSemiring.{0, u_1} Unit R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)) (PowerSeries.{u_1} R) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : PowerSeries.{u_1} R) => R) (RingHom.instFunLike.{u_1, u_1} (PowerSeries.{u_1} R) R (Semiring.toNonAssocSemiring.{u_1} (PowerSeries.{u_1} R) (MvPowerSeries.instSemiring.{0, u_1} Unit R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)) (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)) (PowerSeries.constantCoeff.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3) φ) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_1, u_1, u_1, u_1} R R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3 inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)) (PowerSeries.{u_1} R) R (MvPowerSeries.instAddCommMonoid.{0, u_1} Unit R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3))) (MvPowerSeries.instModule.{0, u_1, u_1} Unit R R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3))) (Semiring.toModule.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)) (Semiring.toModule.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)) (PowerSeries.{u_1} R) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : PowerSeries.{u_1} R) => R) (LinearMap.instFunLike.{u_1, u_1, u_1, u_1} R R (PowerSeries.{u_1} R) R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3 inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3 (MvPowerSeries.instAddCommMonoid.{0, u_1} Unit R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3))) (MvPowerSeries.instModule.{0, u_1, u_1} Unit R R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3))) (Semiring.toModule.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3)) (Semiring.toModule.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3))) (PowerSeries.coeff.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Basic.3213241279._hygCtx._hyg.3 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) φ)","typeFull":"∀ {R : Type u_1} [inst : Semiring R] (φ : PowerSeries R), PowerSeries.constantCoeff φ = (PowerSeries.coeff 0) φ","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] (φ : PowerSeries R), PowerSeries.constantCoeff φ = (PowerSeries.coeff 0) φ","typeReferences":[["PowerSeries"],["RingHom"],["MvPowerSeries","instSemiring"],["LinearMap","instFunLike"],["PowerSeries","constantCoeff"],["MvPowerSeries","instModule"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["RingHom","instFunLike"],["LinearMap"],["DFunLike","coe"],["OfNat","ofNat"],["Unit"],["Nat"],["Semiring","toNonAssocSemiring"],["PowerSeries","coeff"],["instOfNatNat"],["RingHom","id"],["MvPowerSeries","instAddCommMonoid"],["Semiring","toModule"],["Eq"],["Semiring"]],"valueReferences":[["RingHom"],["PowerSeries"],["MvPowerSeries","instSemiring"],["PowerSeries","constantCoeff"],["LinearMap","instFunLike"],["MvPowerSeries","instModule"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["RingHom","instFunLike"],["LinearMap"],["DFunLike","coe"],["OfNat","ofNat"],["Unit"],["Nat"],["PowerSeries","coeff_zero_eq_constantCoeff_apply"],["Semiring","toNonAssocSemiring"],["PowerSeries","coeff"],["instOfNatNat"],["RingHom","id"],["Eq","symm"],["MvPowerSeries","instAddCommMonoid"],["Semiring","toModule"]]},{"isProp":true,"kind":"theorem","name":["PowerSeries","binomialSeries_constantCoeff"],"typeFallback":"forall {R : Type.{u_1}} {A : Type.{u_2}} [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.4 : CommRing.{u_1} R] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.7 : BinomialRing.{u_1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} R (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} R (CommRing.toNonUnitalCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.4))))) (Monoid.toPow.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.4)))))] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10 : Ring.{u_2} A] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.13 : Algebra.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10)] (r : R), Eq.{succ u_2} A (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (RingHom.{u_2, u_2} (PowerSeries.{u_2} A) A (Semiring.toNonAssocSemiring.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instSemiring.{0, u_2} Unit A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10))) (Semiring.toNonAssocSemiring.{u_2} A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10))) (PowerSeries.{u_2} A) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : PowerSeries.{u_2} A) => A) (RingHom.instFunLike.{u_2, u_2} (PowerSeries.{u_2} A) A (Semiring.toNonAssocSemiring.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instSemiring.{0, u_2} Unit A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10))) (Semiring.toNonAssocSemiring.{u_2} A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10))) (PowerSeries.constantCoeff.{u_2} A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10)) (PowerSeries.binomialSeries.{u_1, u_2} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.4 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.7 A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10))) (Algebra.toSMul.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10) inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.13) r)) (OfNat.ofNat.{u_2} A 1 (One.toOfNat1.{u_2} A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1218398397._hygCtx._hyg.10)))))","typeFull":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Ring A] [inst_3 : Algebra R A]\n  (r : R), PowerSeries.constantCoeff (PowerSeries.binomialSeries A r) = 1","typeReadable":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Ring A] [inst_3 : Algebra R A]\n  (r : R), PowerSeries.constantCoeff (PowerSeries.binomialSeries A r) = 1","typeReferences":[["RingHom"],["AddGroupWithOne","toAddMonoidWithOne"],["RingHom","instFunLike"],["CommRing","toNonUnitalCommRing"],["DFunLike","coe"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["Ring","toAddGroupWithOne"],["Monoid","toPow"],["Algebra","toSMul"],["MonoidWithZero","toMonoid"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Eq"],["PowerSeries","binomialSeries"],["PowerSeries"],["CommRing","toCommSemiring"],["MvPowerSeries","instSemiring"],["PowerSeries","constantCoeff"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["CommRing"],["OfNat","ofNat"],["Algebra"],["Ring","toSemiring"],["Unit"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["Ring"],["BinomialRing"]],"valueReferences":[["RingHom"],["Ring","toNonAssocRing"],["Eq","trans"],["AddGroupWithOne","toAddMonoidWithOne"],["PowerSeries","binomialSeries_coeff"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["Ring","toAddGroupWithOne"],["Monoid","toPow"],["RingHom","id"],["DistribMulAction","toMulAction"],["Semiring","toModule"],["NonAssocSemiring","toAddCommMonoidWithOne"],["NonAssocRing","toNonUnitalNonAssocRing"],["instHPow"],["NonUnitalNonAssocSemiring","toDistrib"],["PowerSeries","constantCoeff"],["MulOne","toOne"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap"],["Unit"],["Ring","toSemiring"],["Nat"],["PowerSeries","coeff"],["one_smul"],["AddMonoidWithOne","toOne"],["HSMul","hSMul"],["pow_zero"],["Ring","choose"],["MulOneClass","toMulOne"],["LinearMap","instFunLike"],["RingHom","instFunLike"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["congrArg"],["Algebra","toModule"],["instOfNatNat"],["NonAssocRing","toAddCommGroupWithOne"],["Monoid","toMulOneClass"],["Algebra","toSMul"],["MonoidWithZero","toMonoid"],["instHSMul"],["congrFun'"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocCommRing","toNonAssocRing"],["Eq"],["PowerSeries","binomialSeries"],["PowerSeries"],["Distrib","toAdd"],["CommRing","toCommSemiring"],["MvPowerSeries","instSemiring"],["True"],["instHAdd"],["CommRing","toNonAssocCommRing"],["MvPowerSeries","instModule"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["Semiring","toMonoidWithZero"],["HPow","hPow"],["OfNat","ofNat"],["_private","Mathlib","RingTheory","PowerSeries","Binomial",0,"PowerSeries","binomialSeries_constantCoeff","_simp_1_1"],["HAdd","hAdd"],["eq_self"],["Module","toDistribMulAction"],["AddCommGroupWithOne","toAddGroupWithOne"],["One","toOfNat1"],["of_eq_true"],["Ring","choose_zero_right'"],["MvPowerSeries","instAddCommMonoid"]]},{"isProp":true,"kind":"theorem","name":["PowerSeries","rescale_neg_one_invOneSubPow"],"typeFallback":"forall {A : Type.{u_2}} [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10 : CommRing.{u_2} A] (d : Nat), Eq.{succ u_2} (PowerSeries.{u_2} A) (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (RingHom.{u_2, u_2} (PowerSeries.{u_2} A) (PowerSeries.{u_2} A) (Semiring.toNonAssocSemiring.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instSemiring.{0, u_2} Unit A (CommSemiring.toSemiring.{u_2} A (CommRing.toCommSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10)))) (Semiring.toNonAssocSemiring.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instSemiring.{0, u_2} Unit A (CommSemiring.toSemiring.{u_2} A (CommRing.toCommSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10))))) (PowerSeries.{u_2} A) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : PowerSeries.{u_2} A) => PowerSeries.{u_2} A) (RingHom.instFunLike.{u_2, u_2} (PowerSeries.{u_2} A) (PowerSeries.{u_2} A) (Semiring.toNonAssocSemiring.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instSemiring.{0, u_2} Unit A (CommSemiring.toSemiring.{u_2} A (CommRing.toCommSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10)))) (Semiring.toNonAssocSemiring.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instSemiring.{0, u_2} Unit A (CommSemiring.toSemiring.{u_2} A (CommRing.toCommSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10))))) (PowerSeries.rescale.{u_2} A (CommRing.toCommSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10) (Neg.neg.{u_2} A (NegZeroClass.toNeg.{u_2} A (SubNegZeroMonoid.toNegZeroClass.{u_2} A (SubtractionMonoid.toSubNegZeroMonoid.{u_2} A (SubtractionCommMonoid.toSubtractionMonoid.{u_2} A (AddCommGroup.toDivisionAddCommMonoid.{u_2} A (Ring.toAddCommGroup.{u_2} A (CommRing.toRing.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10))))))) (OfNat.ofNat.{u_2} A 1 (One.toOfNat1.{u_2} A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A (CommRing.toRing.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10)))))))) (Units.val.{u_2} (PowerSeries.{u_2} A) (MonoidWithZero.toMonoid.{u_2} (PowerSeries.{u_2} A) (Semiring.toMonoidWithZero.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instSemiring.{0, u_2} Unit A (CommSemiring.toSemiring.{u_2} A (CommRing.toCommSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10))))) (PowerSeries.invOneSubPow.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10 d))) (PowerSeries.binomialSeries.{0, u_2} Int Int.instCommRing Int.instBinomialRing A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A (CommRing.toRing.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10)))) (SubNegMonoid.toZSMul.{u_2} A (AddGroup.toSubNegMonoid.{u_2} A (AddGroupWithOne.toAddGroup.{u_2} A (Ring.toAddGroupWithOne.{u_2} A (CommRing.toRing.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.12438834._hygCtx._hyg.10))))) (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt d)))","typeFull":"∀ {A : Type u_2} [inst : CommRing A] (d : ℕ),\n  (PowerSeries.rescale (-1)) ↑(PowerSeries.invOneSubPow A d) = PowerSeries.binomialSeries A (-↑d)","typeReadable":"∀ {A : Type u_2} [inst : CommRing A] (d : ℕ),\n  (PowerSeries.rescale (-1)) ↑(PowerSeries.invOneSubPow A d) = PowerSeries.binomialSeries A (-↑d)","typeReferences":[["Int","instCommRing"],["RingHom"],["SubtractionMonoid","toSubNegZeroMonoid"],["Nat","cast"],["Int","instBinomialRing"],["RingHom","instFunLike"],["AddGroupWithOne","toAddMonoidWithOne"],["SubtractionCommMonoid","toSubtractionMonoid"],["DFunLike","coe"],["SubNegZeroMonoid","toNegZeroClass"],["Semiring","toNonAssocSemiring"],["Ring","toAddGroupWithOne"],["PowerSeries","invOneSubPow"],["MonoidWithZero","toMonoid"],["AddGroup","toSubNegMonoid"],["Eq"],["instNatCastInt"],["PowerSeries","binomialSeries"],["PowerSeries"],["CommRing","toCommSemiring"],["MvPowerSeries","instSemiring"],["Neg","neg"],["CommSemiring","toSemiring"],["Semiring","toMonoidWithZero"],["CommRing"],["Int","instNegInt"],["OfNat","ofNat"],["Int"],["Unit"],["Ring","toAddCommGroup"],["CommRing","toRing"],["Nat"],["AddGroupWithOne","toAddGroup"],["PowerSeries","rescale"],["NegZeroClass","toNeg"],["AddCommGroup","toDivisionAddCommMonoid"],["One","toOfNat1"],["Units","val"],["AddMonoidWithOne","toOne"],["SubNegMonoid","toZSMul"]],"valueReferences":[["NonUnitalNonAssocRing","toAddCommGroup"],["instAddNat"],["Int","instSub"],["RingHom"],["SubtractionMonoid","toSubNegZeroMonoid"],["Int","instMonoid"],["Eq","trans"],["Int","instBinomialRing"],["AddGroupWithOne","toAddMonoidWithOne"],["ite_cond_eq_true"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["RingHom","id"],["SubNegMonoid","toSub"],["Eq","symm"],["Eq","ndrec"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Units"],["_private","Mathlib","RingTheory","PowerSeries","Binomial",0,"PowerSeries","rescale_neg_one_invOneSubPow","_proof_1_1"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Mathlib","Tactic","Abel","term_add_constg"],["LinearMap"],["AddCommGroup","toIntModule"],["PowerSeries","coeff_one"],["Ring","toSemiring"],["zsmul_eq_mul"],["PowerSeries","rescale"],["instOfNat"],["PowerSeries","coeff"],["SubtractionMonoid","toSubNegMonoid"],["Units","val"],["Eq","refl"],["AddMonoid","toAddSemigroup"],["eq_false"],["one_smul"],["AddMonoidWithOne","toOne"],["AddCommGroup","toAddCommMonoid"],["zero_smul"],["Int","instCharZero"],["Int","cast_mul","_simp_1"],["Eq","mpr"],["pow_zero"],["AddMonoid","toAddZeroClass"],["MulOneClass","toMulOne"],["LinearMap","instFunLike"],["MulZeroOneClass","toMulOneClass"],["SubtractionCommMonoid","toSubtractionMonoid"],["Int","instRing"],["Int","cast"],["Int","instMul"],["Int","instAddCommGroup"],["instOfNatNat"],["congr"],["Int","instAdd"],["AddCommMagma","toAdd"],["NonAssocCommRing","toNonAssocRing"],["Units","instSMul"],["Eq"],["Mathlib","Tactic","Abel","termg"],["instNatCastInt"],["PowerSeries","binomialSeries"],["Distrib","toAdd"],["ite"],["MvPowerSeries","instModule"],["SubNegMonoid","toNeg"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["mul_one"],["CharP","ofCharZero"],["AddZero","toAdd"],["HPow","hPow"],["Ring","choose_zero_ite"],["OfNat","ofNat"],["Int"],["Nat","cast_add"],["HAdd","hAdd"],["eq_self"],["CommRing","toRing"],["Module","toDistribMulAction"],["AddGroupWithOne","toAddGroup"],["AddCommGroup","toDivisionAddCommMonoid"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["AddGroupWithOne","toIntCast"],["instDecidableEqNat"],["instHSub"],["dite"],["Nat","cast_one"],["Int","instCommRing"],["Int","negOnePow"],["Nat","choose_symm_add"],["PowerSeries","coeff_mk"],["HMul","hMul"],["AddMonoidWithOne","toAddMonoid"],["PowerSeries","binomialSeries_coeff"],["Units","smul_def"],["Mathlib","Tactic","Abel","subst_into_negg"],["Semiring","toNonAssocSemiring"],["PowerSeries","ext"],["Ring","toAddGroupWithOne"],["Monoid","toPow"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["MvPowerSeries","instOne"],["HSub","hSub"],["neg_zero"],["AddGroup","toSubNegMonoid"],["Semiring","toModule"],["NonAssocSemiring","toMulZeroOneClass"],["NonAssocRing","toNonUnitalNonAssocRing"],["AddSemigroup","toAdd"],["DistribSMul","toSMulZeroClass"],["Nat","casesAuxOn"],["instHPow"],["Ring","choose_neg"],["NonUnitalNonAssocSemiring","toDistrib"],["MulOne","toOne"],["Neg","neg"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["add_zero"],["AddZeroClass","toAddZero"],["ite_cond_eq_false"],["Int","instNegInt"],["Unit"],["Units","instOne"],["zero_add"],["Nat"],["AddMonoidWithOne","toNatCast"],["HSMul","hSMul"],["NegZeroClass","toZero"],["id"],["instHMul"],["Int","cast_natCast"],["SubNegMonoid","toZSMul"],["Mathlib","Tactic","Abel","term_atomg"],["AddZero","toZero"],["Ring","choose"],["smul_zero"],["Nat","cast"],["Mathlib","Tactic","Abel","subst_into_addg"],["RingHom","instFunLike"],["CommRing","toNonUnitalCommRing"],["DFunLike","coe"],["SubNegZeroMonoid","toNegZeroClass"],["congrArg"],["PowerSeries","invOneSubPow"],["PowerSeries","coeff_rescale"],["NonAssocRing","toAddCommGroupWithOne"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["congrFun'"],["Zero","toOfNat0"],["instMulActionIntOfSubtractionMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Int","cast_negOnePow_natCast"],["Nat","choose"],["PowerSeries"],["CommRing","toCommSemiring"],["MvPowerSeries","instSemiring"],["True"],["instHAdd"],["CommRing","toNonAssocCommRing"],["Monoid","PowAssoc"],["CommSemiring","toSemiring"],["Distrib","toMul"],["Semiring","toMonoidWithZero"],["Ring","choose_natCast"],["neg_add_rev"],["Mathlib","Tactic","Abel","term_neg"],["instSMulWithZeroInt"],["Ring","toAddCommGroup"],["AddCommGroupWithOne","toAddGroupWithOne"],["NegZeroClass","toNeg"],["AddCommMonoid","toAddCommSemigroup"],["SubNegMonoid","toAddMonoid"],["One","toOfNat1"],["of_eq_true"],["Int","cast_mul"],["Int","instSemiring"],["CharP","cast_eq_zero"],["Mathlib","Tactic","Abel","const_add_termg"],["Ring","choose_zero_right'"],["MvPowerSeries","instAddCommMonoid"],["Int","instAddMonoid"]]},{"isProp":true,"kind":"theorem","name":["PowerSeries","binomialSeries_nat"],"typeFallback":"forall {R : Type.{u_1}} {A : Type.{u_2}} [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.4 : CommRing.{u_1} R] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.7 : BinomialRing.{u_1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} R (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} R (CommRing.toNonUnitalCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.4))))) (Monoid.toPow.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.4)))))] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.10 : Ring.{u_2} A] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.13 : Algebra.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.10)] (d : Nat), Eq.{succ u_2} (PowerSeries.{u_2} A) (PowerSeries.binomialSeries.{u_1, u_2} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.4 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.7 A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.10))) (Algebra.toSMul.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.10) inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.13) (Nat.cast.{u_1} R (AddMonoidWithOne.toNatCast.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R (CommRing.toRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.4)))) d)) (HPow.hPow.{u_2, 0, u_2} (PowerSeries.{u_2} A) Nat (PowerSeries.{u_2} A) (instHPow.{u_2, 0} (PowerSeries.{u_2} A) Nat (Monoid.toPow.{u_2} (PowerSeries.{u_2} A) (MonoidWithZero.toMonoid.{u_2} (PowerSeries.{u_2} A) (Semiring.toMonoidWithZero.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instSemiring.{0, u_2} Unit A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.10)))))) (HAdd.hAdd.{u_2, u_2, u_2} (PowerSeries.{u_2} A) (PowerSeries.{u_2} A) (PowerSeries.{u_2} A) (instHAdd.{u_2} (PowerSeries.{u_2} A) (Distrib.toAdd.{u_2} (PowerSeries.{u_2} A) (NonUnitalNonAssocSemiring.toDistrib.{u_2} (PowerSeries.{u_2} A) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} (PowerSeries.{u_2} A) (NonAssocRing.toNonUnitalNonAssocRing.{u_2} (PowerSeries.{u_2} A) (Ring.toNonAssocRing.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instRing.{0, u_2} Unit A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.10))))))) (OfNat.ofNat.{u_2} (PowerSeries.{u_2} A) 1 (One.toOfNat1.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instOne.{0, u_2} Unit A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.10)))) (PowerSeries.X.{u_2} A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.1191813712._hygCtx._hyg.10))) d)","typeFull":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Ring A] [inst_3 : Algebra R A]\n  (d : ℕ), PowerSeries.binomialSeries A ↑d = (1 + PowerSeries.X) ^ d","typeReadable":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Ring A] [inst_3 : Algebra R A]\n  (d : ℕ), PowerSeries.binomialSeries A ↑d = (1 + PowerSeries.X) ^ d","typeReferences":[["PowerSeries","X"],["Ring","toNonAssocRing"],["Nat","cast"],["AddGroupWithOne","toAddMonoidWithOne"],["CommRing","toNonUnitalCommRing"],["MvPowerSeries","instRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Monoid","toPow"],["Ring","toAddGroupWithOne"],["MvPowerSeries","instOne"],["MonoidWithZero","toMonoid"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Algebra","toSMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["PowerSeries","binomialSeries"],["instHPow"],["PowerSeries"],["Distrib","toAdd"],["CommRing","toCommSemiring"],["MvPowerSeries","instSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["instHAdd"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["HPow","hPow"],["CommRing"],["OfNat","ofNat"],["Unit"],["Algebra"],["Ring","toSemiring"],["HAdd","hAdd"],["CommRing","toRing"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["Ring"],["BinomialRing"]],"valueReferences":[["Polynomial","instAdd"],["Ring","toNonAssocRing"],["Eq","trans"],["HMul","hMul"],["AddGroupWithOne","toAddMonoidWithOne"],["AddMonoidWithOne","toAddMonoid"],["PowerSeries","binomialSeries_coeff"],["MvPowerSeries","instRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["PowerSeries","ext"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["Ring","toAddGroupWithOne"],["RingHom","id"],["MvPowerSeries","instOne"],["Semiring","toModule"],["NonAssocSemiring","toAddCommMonoidWithOne"],["NonAssocSemiring","toMulZeroOneClass"],["NonAssocRing","toNonUnitalNonAssocRing"],["Polynomial","toPowerSeries"],["instHPow"],["Polynomial","coe_X"],["Polynomial","coeff"],["NonUnitalNonAssocSemiring","toDistrib"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Polynomial","coe_pow"],["LinearMap"],["Polynomial","instOne"],["Unit"],["Ring","toSemiring"],["Polynomial"],["Nat"],["AddMonoidWithOne","toNatCast"],["AddMonoid","toNSMul"],["PowerSeries","coeff"],["HSMul","hSMul"],["AddMonoidWithOne","toOne"],["id"],["instHMul"],["Eq","mpr"],["Polynomial","coeff_coe"],["Polynomial","coe_add"],["Ring","choose"],["PowerSeries","X"],["Nat","cast"],["LinearMap","instFunLike"],["Polynomial","coeff_one_add_X_pow"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["congrArg"],["Algebra","toModule"],["NonAssocRing","toAddCommGroupWithOne"],["congr"],["MonoidWithZero","toMonoid"],["Algebra","toSMul"],["instHSMul"],["congrFun'"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocCommRing","toNonAssocRing"],["Eq"],["Nat","choose"],["PowerSeries","binomialSeries"],["PowerSeries"],["Distrib","toAdd"],["CommRing","toCommSemiring"],["Polynomial","X"],["MvPowerSeries","instSemiring"],["True"],["CommRing","toNonAssocCommRing"],["instHAdd"],["Monoid","PowAssoc"],["MvPowerSeries","instModule"],["Distrib","toMul"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["mul_one"],["Ring","choose_natCast"],["Polynomial","semiring"],["Polynomial","coe_one"],["HPow","hPow"],["OfNat","ofNat"],["HAdd","hAdd"],["eq_self"],["CommRing","toRing"],["AddCommGroupWithOne","toAddGroupWithOne"],["One","toOfNat1"],["of_eq_true"],["Nat","cast_smul_eq_nsmul"],["nsmul_eq_mul"],["MvPowerSeries","instAddCommMonoid"]]},{"isProp":true,"kind":"theorem","name":["PowerSeries","binomialSeries_add"],"typeFallback":"forall {R : Type.{u_1}} {A : Type.{u_2}} [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4 : CommRing.{u_1} R] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.7 : BinomialRing.{u_1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} R (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} R (CommRing.toNonUnitalCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4))))) (Monoid.toPow.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4)))))] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10 : Ring.{u_2} A] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.13 : Algebra.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10)] (r : R) (s : R), Eq.{succ u_2} (PowerSeries.{u_2} A) (PowerSeries.binomialSeries.{u_1, u_2} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.7 A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10))) (Algebra.toSMul.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10) inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.13) (HAdd.hAdd.{u_1, u_1, u_1} R R R (instHAdd.{u_1} R (Distrib.toAdd.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} R (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} R (CommRing.toNonUnitalCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4))))))) r s)) (HMul.hMul.{u_2, u_2, u_2} (PowerSeries.{u_2} A) (PowerSeries.{u_2} A) (PowerSeries.{u_2} A) (instHMul.{u_2} (PowerSeries.{u_2} A) (MvPowerSeries.instMul.{0, u_2} Unit A (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10))) (PowerSeries.binomialSeries.{u_1, u_2} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.7 A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10))) (Algebra.toSMul.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10) inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.13) r) (PowerSeries.binomialSeries.{u_1, u_2} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.7 A (AddMonoidWithOne.toOne.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10))) (Algebra.toSMul.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.10) inst._@.Mathlib.RingTheory.PowerSeries.Binomial.3695793336._hygCtx._hyg.13) s))","typeFull":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Ring A] [inst_3 : Algebra R A]\n  (r s : R), PowerSeries.binomialSeries A (r + s) = PowerSeries.binomialSeries A r * PowerSeries.binomialSeries A s","typeReadable":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Ring A] [inst_3 : Algebra R A]\n  (r s : R), PowerSeries.binomialSeries A (r + s) = PowerSeries.binomialSeries A r * PowerSeries.binomialSeries A s","typeReferences":[["MvPowerSeries","instMul"],["HMul","hMul"],["AddGroupWithOne","toAddMonoidWithOne"],["CommRing","toNonUnitalCommRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Monoid","toPow"],["Ring","toAddGroupWithOne"],["MonoidWithZero","toMonoid"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Algebra","toSMul"],["Eq"],["PowerSeries","binomialSeries"],["PowerSeries"],["CommRing","toCommSemiring"],["Distrib","toAdd"],["NonUnitalNonAssocSemiring","toDistrib"],["instHAdd"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["CommRing"],["Unit"],["Algebra"],["Ring","toSemiring"],["HAdd","hAdd"],["AddMonoidWithOne","toOne"],["instHMul"],["Ring"],["BinomialRing"]],"valueReferences":[["Ring","toNonAssocRing"],["Finset"],["Eq","trans"],["AddGroupWithOne","toAddMonoidWithOne"],["SemigroupAction","toSMul"],["SMulZeroClass","toSMul"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["RingHom","id"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocCommSemiring"],["mul_comm"],["Finset","sum"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Ring","add_choose_eq"],["rfl"],["NonUnitalCommSemiring","toNonUnitalSemiring"],["Finset","HasAntidiagonal","antidiagonal"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Algebra","mul_smul_comm"],["Prod","snd"],["LinearMap"],["Ring","toSemiring"],["Prod"],["PowerSeries","coeff"],["Eq","refl"],["AddMonoidWithOne","toOne"],["Eq","mpr"],["AddMonoid","toAddZeroClass"],["LinearMap","instFunLike"],["MvPowerSeries","instMul"],["NonUnitalNonAssocCommSemiring","toCommMagma"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["Semigroup","toMul"],["Prod","fst"],["congr"],["NonAssocCommRing","toNonAssocRing"],["Eq"],["PowerSeries","binomialSeries"],["Nat","instAddMonoid"],["Distrib","toAdd"],["Commute","all"],["MvPowerSeries","instModule"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["mul_one"],["OfNat","ofNat"],["HAdd","hAdd"],["CommRing","toRing"],["Module","toDistribMulAction"],["HMul","hMul"],["NonUnitalSemiring","toSemigroupWithZero"],["PowerSeries","binomialSeries_coeff"],["Finset","Nat","instHasAntidiagonal"],["Semiring","toNonAssocSemiring"],["PowerSeries","ext"],["Ring","toAddGroupWithOne"],["Monoid","toPow"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["DistribMulAction","toMulAction"],["Semiring","toModule"],["NonAssocRing","toNonUnitalNonAssocRing"],["NonAssocSemiring","toMulZeroOneClass"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toDistrib"],["CommMagma","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Finset","sum_smul"],["NonUnitalCommRing","toNonUnitalCommSemiring"],["AddZeroClass","toAddZero"],["Unit"],["Nat"],["HSMul","hSMul"],["id"],["instHMul"],["AddZero","toZero"],["Ring","choose"],["CommRing","toNonUnitalCommRing"],["DFunLike","coe"],["congrArg"],["Finset","sum_congr"],["PowerSeries","coeff_mul"],["Algebra","toModule"],["NonAssocRing","toAddCommGroupWithOne"],["Algebra","toSMul"],["MonoidWithZero","toMonoid"],["instHSMul"],["congrFun'"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["SemigroupAction","mul_smul"],["PowerSeries"],["CommRing","toCommSemiring"],["instHAdd"],["CommRing","toNonAssocCommRing"],["CommSemiring","toSemiring"],["Distrib","toMul"],["Semiring","toMonoidWithZero"],["One","toOfNat1"],["MvPowerSeries","instAddCommMonoid"],["SemigroupWithZero","toSemigroup"],["MulAction","toSemigroupAction"]]},{"isProp":false,"kind":"definition","name":["PowerSeries","binomialSeries"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.382820647._hygCtx._hyg.4 : CommRing.{u_1} R] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.382820647._hygCtx._hyg.7 : BinomialRing.{u_1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} R (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} R (CommRing.toNonUnitalCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.382820647._hygCtx._hyg.4))))) (Monoid.toPow.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.382820647._hygCtx._hyg.4)))))] (A : Type.{u_3}) [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.382820647._hygCtx._hyg.11 : One.{u_3} A] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.382820647._hygCtx._hyg.14 : SMul.{u_1, u_3} R A], R -> (PowerSeries.{u_3} A)","typeFull":"{R : Type u_1} → [inst : CommRing R] → [BinomialRing R] → (A : Type u_3) → [One A] → [SMul R A] → R → PowerSeries A","typeReadable":"{R : Type u_1} → [inst : CommRing R] → [BinomialRing R] → (A : Type u_3) → [One A] → [SMul R A] → R → PowerSeries A","typeReferences":[["PowerSeries"],["CommRing","toCommSemiring"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["Semiring","toMonoidWithZero"],["CommRing","toNonUnitalCommRing"],["CommRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["SMul"],["Monoid","toPow"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["MonoidWithZero","toMonoid"],["One"],["BinomialRing"]],"valueReferences":[["PowerSeries","mk"],["CommRing","toCommSemiring"],["CommRing","toNonAssocCommRing"],["CommSemiring","toSemiring"],["Semiring","toMonoidWithZero"],["OfNat","ofNat"],["One","toOfNat1"],["Monoid","toPow"],["NonAssocRing","toAddCommGroupWithOne"],["HSMul","hSMul"],["MonoidWithZero","toMonoid"],["instHSMul"],["NonAssocCommRing","toNonAssocRing"],["Ring","choose"]]},{"isProp":true,"kind":"theorem","name":["PowerSeries","binomialSeries_coeff"],"typeFallback":"forall {R : Type.{u_1}} {A : Type.{u_2}} [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.4 : CommRing.{u_1} R] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.7 : BinomialRing.{u_1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} R (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} R (CommRing.toNonUnitalCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.4))))) (Monoid.toPow.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.4)))))] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10 : Semiring.{u_2} A] [inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.13 : SMul.{u_1, u_2} R A] (r : R) (n : Nat), Eq.{succ u_2} A (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (LinearMap.{u_2, u_2, u_2, u_2} A A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10 (RingHom.id.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10)) (PowerSeries.{u_2} A) A (MvPowerSeries.instAddCommMonoid.{0, u_2} Unit A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10))) (MvPowerSeries.instModule.{0, u_2, u_2} Unit A A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10))) (Semiring.toModule.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10)) (Semiring.toModule.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10)) (PowerSeries.{u_2} A) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : PowerSeries.{u_2} A) => A) (LinearMap.instFunLike.{u_2, u_2, u_2, u_2} A A (PowerSeries.{u_2} A) A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10 (MvPowerSeries.instAddCommMonoid.{0, u_2} Unit A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10))) (MvPowerSeries.instModule.{0, u_2, u_2} Unit A A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10))) (Semiring.toModule.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10)) (Semiring.toModule.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10) (RingHom.id.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10))) (PowerSeries.coeff.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10 n) (PowerSeries.binomialSeries.{u_1, u_2} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.4 inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.7 A (AddMonoidWithOne.toOne.{u_2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10)))) inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.13 r)) (HSMul.hSMul.{u_1, u_2, u_2} R A A (instHSMul.{u_1, u_2} R A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.13) (Ring.choose.{u_1} R (NonAssocRing.toAddCommGroupWithOne.{u_1} R (NonAssocCommRing.toNonAssocRing.{u_1} R (CommRing.toNonAssocCommRing.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.4))) (Monoid.toPow.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.4))))) inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.7 r n) (OfNat.ofNat.{u_2} A 1 (One.toOfNat1.{u_2} A (AddMonoidWithOne.toOne.{u_2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.RingTheory.PowerSeries.Binomial.848845954._hygCtx._hyg.10)))))))","typeFull":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Semiring A] [inst_3 : SMul R A]\n  (r : R) (n : ℕ), (PowerSeries.coeff n) (PowerSeries.binomialSeries A r) = Ring.choose r n • 1","typeReadable":"∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : BinomialRing R] [inst_2 : Semiring A] [inst_3 : SMul R A]\n  (r : R) (n : ℕ), (PowerSeries.coeff n) (PowerSeries.binomialSeries A r) = Ring.choose r n • 1","typeReferences":[["LinearMap","instFunLike"],["CommRing","toNonUnitalCommRing"],["DFunLike","coe"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["SMul"],["Semiring","toNonAssocSemiring"],["Monoid","toPow"],["RingHom","id"],["NonAssocRing","toAddCommGroupWithOne"],["MonoidWithZero","toMonoid"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["instHSMul"],["NonAssocCommRing","toNonAssocRing"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Semiring","toModule"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["PowerSeries","binomialSeries"],["PowerSeries"],["CommRing","toCommSemiring"],["CommRing","toNonAssocCommRing"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["MvPowerSeries","instModule"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Semiring","toMonoidWithZero"],["CommRing"],["LinearMap"],["OfNat","ofNat"],["Unit"],["Nat"],["One","toOfNat1"],["PowerSeries","coeff"],["HSMul","hSMul"],["AddMonoidWithOne","toOne"],["MvPowerSeries","instAddCommMonoid"],["Ring","choose"],["Semiring"],["BinomialRing"]],"valueReferences":[["CommRing","toCommSemiring"],["PowerSeries","coeff_mk"],["CommRing","toNonAssocCommRing"],["CommSemiring","toSemiring"],["Semiring","toMonoidWithZero"],["OfNat","ofNat"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["Monoid","toPow"],["NonAssocRing","toAddCommGroupWithOne"],["AddMonoidWithOne","toOne"],["HSMul","hSMul"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocCommRing","toNonAssocRing"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Ring","choose"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.TensorProduct.DirectLimitFG.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5972c568d6fb98196ec4cb29d243c54fdd95a6f6e598f86ada6952d5a9b3c0ac
+size 23373518