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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Group.Finset.Interval.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Group.Finset.Preimage.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.NatAntidiagonal.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Sym.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.DirectSum.AddChar.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Field.Action.ConjAct.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Submonoid.Finite.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.UniqueProds.VectorSpace.sym.json

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

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Submonoid.Primal.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Units.Equiv.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.sym.json

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(IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (instIsLeftCancelAddOfAddLeftReflectLE.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_lt_of_covariant_le.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) => HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26) Int.instLinearOrder Int.instAddLeftMono)))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing))))) (HomologicalComplex.instCategory.{v, u, 0} Int C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.6)) (ComplexShape.up.{0} Int Int.instAdd (instIsRightCancelAddOfAddRightReflectLE.{0} Int Int.instAdd (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_swap_add_of_contravariant_add.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) => LE.le.{0} Int (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41) Int.instAddCommSemigroup (IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (instIsLeftCancelAddOfAddLeftReflectLE.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_lt_of_covariant_le.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) => HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26) Int.instLinearOrder Int.instAddLeftMono)))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing))))) (HomologicalComplex.quasiIso.{v, u, 0} Int C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.6)) (ComplexShape.up.{0} Int Int.instAdd (instIsRightCancelAddOfAddRightReflectLE.{0} Int Int.instAdd (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_swap_add_of_contravariant_add.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) => LE.le.{0} Int (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41) Int.instAddCommSemigroup (IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (instIsLeftCancelAddOfAddLeftReflectLE.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_lt_of_covariant_le.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) => HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26) Int.instLinearOrder Int.instAddLeftMono)))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing)))) (CategoryTheory.categoryWithHomology_of_abelian.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.6)) Int Int.instAddMonoid (CochainComplex.instHasShiftInt.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.2910590382._hygCtx._hyg.6)) K L","typeFull":"∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] [CategoryTheory.HasExt C]\n  (K L : CochainComplex C ℤ) [K.IsGE 0] [K.IsLE 0] [L.IsGE 0] [L.IsLE 0],\n  CategoryTheory.Localization.HasSmallLocalizedShiftedHom (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) ℤ K L","typeReadable":"∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] [CategoryTheory.HasExt C]\n  (K L : CochainComplex C ℤ) [K.IsGE 0] [K.IsLE 0] [L.IsGE 0] [L.IsLE 0],\n  CategoryTheory.Localization.HasSmallLocalizedShiftedHom (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) ℤ K L","typeReferences":[["instIsRightCancelAddOfAddRightReflectLE"],["contravariant_swap_add_of_contravariant_add"],["PartialOrder","toPreorder"],["CochainComplex","IsLE"],["AddGroupWithOne","toAddMonoidWithOne"],["CategoryTheory","HasExt"],["AddCancelMonoid","toAddRightCancelMonoid"],["Ring","toAddGroupWithOne"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["HomologicalComplex"],["Int","instAddGroup"],["SemilatticeInf","toPartialOrder"],["instLatticeInt"],["CategoryTheory","Abelian"],["AddGroup","toAddCancelMonoid"],["CategoryTheory","categoryWithHomology_of_abelian"],["AddRightCancelMonoid","toAddRightCancelSemigroup"],["HomologicalComplex","instCategory"],["CategoryTheory","Localization","HasSmallLocalizedShiftedHom"],["CategoryTheory","Abelian","toPreadditive"],["instOfNat"],["AddMonoidWithOne","toOne"],["instIsLeftCancelAddOfAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["Int","instAddCommMonoid"],["CochainComplex","IsGE"],["ComplexShape","up"],["Int","instAddCommSemigroup"],["CategoryTheory","Category"],["Int","instRing"],["CochainComplex"],["contravariant_lt_of_covariant_le"],["Int","instAdd"],["Int","instIsStrictOrderedRing"],["Int","instAddLeftMono"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["CochainComplex","instHasShiftInt"],["Preorder","toLE"],["IsLeftCancelAdd","addLeftReflectLE_of_addLeftReflectLT"],["IsStrictOrderedRing","toIsOrderedCancelAddMonoid"],["Int","instLinearOrder"],["Lattice","toSemilatticeInf"],["instHAdd"],["HomologicalComplex","quasiIso"],["OfNat","ofNat"],["Int"],["HAdd","hAdd"],["Int","instSemiring"],["LE","le"],["Int","instAddMonoid"]],"valueReferences":[["instOfNat"],["CategoryTheory","HasExt","hasSmallLocalizedShiftedHom_of_isLE_of_isGE"],["OfNat","ofNat"],["Int"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","HasExt","hasSmallLocalizedShiftedHom_of_isLE_of_isGE"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6 : CategoryTheory.Abelian.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3] [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.9 : CategoryTheory.HasExt.{w, v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6] (K : CochainComplex.{v, u, 0} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6)) Int (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Int (AddCancelMonoid.toAddRightCancelMonoid.{0} Int (AddGroup.toAddCancelMonoid.{0} Int Int.instAddGroup))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing)))) (L : CochainComplex.{v, u, 0} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6)) Int (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Int (AddCancelMonoid.toAddRightCancelMonoid.{0} Int (AddGroup.toAddCancelMonoid.{0} Int Int.instAddGroup))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing)))) (a : Int) (b : Int) [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.28 : CochainComplex.IsGE.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6)) K a] [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.31 : CochainComplex.IsLE.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6)) K a] [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.34 : CochainComplex.IsGE.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6)) L b] [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.37 : CochainComplex.IsLE.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6)) L b], CategoryTheory.Localization.HasSmallLocalizedShiftedHom.{w, 0, v, max u v} (HomologicalComplex.{v, u, 0} Int C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6)) (ComplexShape.up.{0} Int Int.instAdd (instIsRightCancelAddOfAddRightReflectLE.{0} Int Int.instAdd (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_swap_add_of_contravariant_add.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) => LE.le.{0} Int (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41) Int.instAddCommSemigroup (IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (instIsLeftCancelAddOfAddLeftReflectLE.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_lt_of_covariant_le.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) => HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26) Int.instLinearOrder Int.instAddLeftMono)))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing))))) (HomologicalComplex.instCategory.{v, u, 0} Int C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Ext.TStructure.235196262._hygCtx._hyg.6)) (ComplexShape.up.{0} Int Int.instAdd (instIsRightCancelAddOfAddRightReflectLE.{0} Int Int.instAdd (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_swap_add_of_contravariant_add.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) => LE.le.{0} Int (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41) Int.instAddCommSemigroup (IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (instIsLeftCancelAddOfAddLeftReflectLE.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.Embedding.Boundary.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.HasNoLoop.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Card.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.PUnit.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Submodule.Basic.sym.json

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(AddZero.toZero.{v} M (AddZeroClass.toAddZero.{v} M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.10)))) (DistribSMul.toSMulZeroClass.{u, v} R M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.10)) (DistribMulAction.toDistribSMul.{u, v} R M (MonoidWithZero.toMonoid.{u} R (Semiring.toMonoidWithZero.{u} R inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.7)) (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.10) (Module.toDistribMulAction.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.10 module_M)))) inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.29] 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inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.38 inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.45 inst._@.Mathlib.Algebra.Module.Submodule.Basic.907309249._hygCtx._hyg.52)","typeFull":"∀ {S : Type u'} {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] {module_M : Module R M}\n  (p : Submodule R M) [inst_2 : SMul S R] [inst_3 : SMul S M] [inst_4 : IsScalarTower S R M] [inst_5 : SMul Sᵐᵒᵖ R]\n  [inst_6 : SMul Sᵐᵒᵖ M] [inst_7 : IsScalarTower Sᵐᵒᵖ R M] [IsCentralScalar S M], IsCentralScalar S ↥p","typeReadable":"∀ {S : Type u'} {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] {module_M : Module R M}\n  (p : Submodule R M) [inst_2 : SMul S R] [inst_3 : SMul S M] [inst_4 : IsScalarTower S R M] [inst_5 : SMul Sᵐᵒᵖ R]\n  [inst_6 : SMul Sᵐᵒᵖ M] [inst_7 : IsScalarTower Sᵐᵒᵖ R M] [IsCentralScalar S M], IsCentralScalar S ↥p","typeReferences":[["SetLike","instMembership"],["Subtype"],["Module"],["IsScalarTower"],["Membership","mem"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["Submodule"],["MulOpposite"],["Module","toDistribMulAction"],["AddCommMonoid"],["SMul"],["Submodule","setLike"],["IsCentralScalar"],["MonoidWithZero","toMonoid"],["Submodule","smul"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]],"valueReferences":[["Submodule","toSubMulAction"],["Module","toDistribMulAction"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Semiring","toMonoidWithZero"],["SubMulAction","isCentralScalar"],["AddCommMonoid","toAddMonoid"]]},{"isProp":true,"kind":"theorem","name":["Submodule","smul_mem_iff"],"typeFallback":"forall {S : Type.{u'}} {R : Type.{u}} {M : Type.{v}} [inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.7 : DivisionSemiring.{u'} S] [inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.10 : Semiring.{u} R] [inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13 : AddCommMonoid.{v} M] [inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.16 : Module.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.20 : SMul.{u', u} S R] [inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.24 : Module.{u', v} S M (DivisionSemiring.toSemiring.{u'} S inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13] [inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.28 : IsScalarTower.{u', u, v} S R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.20 (SMulZeroClass.toSMul.{u, v} R M (AddZero.toZero.{v} M (AddZeroClass.toAddZero.{v} M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u, v} R M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u, v} R M (MonoidWithZero.toMonoid.{u} R (Semiring.toMonoidWithZero.{u} R inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.10)) (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13) (Module.toDistribMulAction.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.16)))) (SMulZeroClass.toSMul.{u', v} S M (AddZero.toZero.{v} M (AddZeroClass.toAddZero.{v} M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u', v} S M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13)) (DistribMulAction.toDistribSMul.{u', v} S M (MonoidWithZero.toMonoid.{u'} S (Semiring.toMonoidWithZero.{u'} S (DivisionSemiring.toSemiring.{u'} S inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.7))) (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13) (Module.toDistribMulAction.{u', v} S M (DivisionSemiring.toSemiring.{u'} S inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.24))))] (p : Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.16) {s : S} {x : M}, (Ne.{succ u'} S s (OfNat.ofNat.{u'} S 0 (Zero.toOfNat0.{u'} S (MulZeroClass.toZero.{u'} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u'} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u'} S (Semiring.toNonAssocSemiring.{u'} S (DivisionSemiring.toSemiring.{u'} S inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.7)))))))) -> (Iff (Membership.mem.{v, v} M (Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.16) (SetLike.instMembership.{v, v} (Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.16) M (Submodule.setLike.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.16)) p (HSMul.hSMul.{u', v, v} S M M (instHSMul.{u', v} S M (SMulZeroClass.toSMul.{u', v} S M (AddZero.toZero.{v} M (AddZeroClass.toAddZero.{v} M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.97566365._hygCtx._hyg.13)))) (DistribSMul.toSMulZeroClass.{u', v} S M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M 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[IsScalarTower S R M] (p : Submodule R M) {s : S}\n  {x : M}, s ≠ 0 → (s • x ∈ p ↔ x ∈ 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{R : Type.{u}} {M : Type.{v}} [inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.7 : Semiring.{u} R] [inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.10 : AddCommMonoid.{v} M] [inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.13 : Module.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.10], Monotone.{v, v} (Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.13) (SubMulAction.{u, v} R M (SMulZeroClass.toSMul.{u, v} R M (AddZero.toZero.{v} M (AddZeroClass.toAddZero.{v} M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.10)))) (DistribSMul.toSMulZeroClass.{u, v} R M (AddMonoid.toAddZeroClass.{v} M (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.10)) (DistribMulAction.toDistribSMul.{u, v} R M (MonoidWithZero.toMonoid.{u} R (Semiring.toMonoidWithZero.{u} R inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.7)) (AddCommMonoid.toAddMonoid.{v} M inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.10) (Module.toDistribMulAction.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.13))))) (PartialOrder.toPreorder.{v} (Submodule.{u, v} R M inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Submodule.Basic.1681182752._hygCtx._hyg.10 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.MvPolynomial.Counit.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.MvPolynomial.Invertible.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.sym.json

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{ι : Type.{u_1}} {R : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.3755482419._hygCtx._hyg.5 : CommMonoidWithZero.{u_2} R] [inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.3755482419._hygCtx._hyg.8 : PartialOrder.{u_2} R] [inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.3755482419._hygCtx._hyg.11 : ZeroLEOneClass.{u_2} R (MulZeroClass.toZero.{u_2} R (MulZeroOneClass.toMulZeroClass.{u_2} R (MonoidWithZero.toMulZeroOneClass.{u_2} R (CommMonoidWithZero.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.3755482419._hygCtx._hyg.5)))) (MulOne.toOne.{u_2} R (MulOneClass.toMulOne.{u_2} R (MulZeroOneClass.toMulOneClass.{u_2} R (MonoidWithZero.toMulZeroOneClass.{u_2} R (CommMonoidWithZero.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.3755482419._hygCtx._hyg.5))))) (Preorder.toLE.{u_2} R (PartialOrder.toPreorder.{u_2} R 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(forall (i : ι), (Membership.mem.{u_1, u_1} ι (Finset.{u_1} ι) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} ι) ι (Finset.instSetLike.{u_1} ι)) s i) -> (LT.lt.{u_2} R (Preorder.toLT.{u_2} R (PartialOrder.toPreorder.{u_2} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.3755482419._hygCtx._hyg.8)) (OfNat.ofNat.{u_2} R 0 (Zero.toOfNat0.{u_2} R (MulZeroClass.toZero.{u_2} R (MulZeroOneClass.toMulZeroClass.{u_2} R (MonoidWithZero.toMulZeroOneClass.{u_2} R (CommMonoidWithZero.toMonoidWithZero.{u_2} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.3755482419._hygCtx._hyg.5)))))) (f i))) -> (forall (i : ι), (Membership.mem.{u_1, u_1} ι (Finset.{u_1} ι) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} ι) ι (Finset.instSetLike.{u_1} ι)) s i) -> (LT.lt.{u_2} R (Preorder.toLT.{u_2} R (PartialOrder.toPreorder.{u_2} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset.3755482419._hygCtx._hyg.8)) (f i) (g i))) -> (Finset.Nonempty.{u_1} ι s) -> 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