Documentation Verification Report

Basic

📁 Source: Mathlib/Algebra/Homology/Embedding/Basic.lean

Statistics

MetricCount
DefinitionsIsRelIff, IsTruncGE, IsTruncLE, f, mk', op, r, embeddingDown'Add, embeddingDownNat, embeddingUp'Add, embeddingUpIntGE, embeddingUpIntLE, embeddingUpNat
13
Theoremsrel', mem_next, toIsRelIff, mem_prev, toIsRelIff, f_eq_of_r_eq_some, injective_f, instIsRelIffMk', instIsRelIffOp, instIsTruncGEOpOfIsTruncLE, instIsTruncLEOpOfIsTruncGE, mem_next, mem_prev, mk'_f, op_f, r_eq_none, r_eq_some, r_f, rel, rel_iff, embeddingDown'Add_f, embeddingDownNat_f, embeddingUp'Add_f, embeddingUpIntGE_f, embeddingUpIntLE_f, embeddingUpNat_f, instIsRelIffEmbeddingDown'Add, instIsRelIffEmbeddingUp'Add, instIsRelIffNatIntEmbeddingDownNat, instIsRelIffNatIntEmbeddingUpIntGE, instIsRelIffNatIntEmbeddingUpIntLE, instIsRelIffNatIntEmbeddingUpNat, instIsTruncGEEmbeddingUp'Add, instIsTruncGENatIntEmbeddingUpIntGE, instIsTruncGENatIntEmbeddingUpNat, instIsTruncLEEmbeddingDown'Add, instIsTruncLENatIntEmbeddingDownNat, instIsTruncLENatIntEmbeddingUpIntLE, notMem_range_embeddingUpIntGE_iff, notMem_range_embeddingUpIntLE_iff
40
Total53

ComplexShape

Definitions

NameCategoryTheorems
embeddingDown'Add 📖CompOp
3 mathmath: instIsTruncLEEmbeddingDown'Add, embeddingDown'Add_f, instIsRelIffEmbeddingDown'Add
embeddingDownNat 📖CompOp
4 mathmath: CochainComplex.instIsStrictlyLEExtendNatIntEmbeddingDownNatOfNat, instIsRelIffNatIntEmbeddingDownNat, embeddingDownNat_f, instIsTruncLENatIntEmbeddingDownNat
embeddingUp'Add 📖CompOp
3 mathmath: embeddingUp'Add_f, instIsTruncGEEmbeddingUp'Add, instIsRelIffEmbeddingUp'Add
embeddingUpIntGE 📖CompOp
12 mathmath: CochainComplex.quasiIsoAt_πTruncGE, CochainComplex.instQuasiIsoAtIntπTruncGE, Embedding.embeddingUpInt_areComplementary, instIsTruncGENatIntEmbeddingUpIntGE, CochainComplex.quasiIso_truncGEMap_iff, instIsRelIffNatIntEmbeddingUpIntGE, boundaryGE_embeddingUpIntGE_iff, CochainComplex.quasiIso_πTruncGE_iff, CochainComplex.ConnectData.restrictionGEIso_inv_f, embeddingUpIntGE_f, CochainComplex.instQuasiIsoIntπTruncGEOfIsGE, CochainComplex.ConnectData.restrictionGEIso_hom_f
embeddingUpIntLE 📖CompOp
12 mathmath: CochainComplex.quasiIso_truncLEMap_iff, instIsTruncLENatIntEmbeddingUpIntLE, instIsRelIffNatIntEmbeddingUpIntLE, Embedding.embeddingUpInt_areComplementary, CochainComplex.instQuasiIsoAtIntιTruncLE, CochainComplex.quasiIsoAt_ιTruncLE, CochainComplex.ConnectData.restrictionLEIso_inv_f, CochainComplex.instQuasiIsoIntιTruncLEOfIsLE, CochainComplex.ConnectData.restrictionLEIso_hom_f, CochainComplex.quasiIso_ιTruncLE_iff, embeddingUpIntLE_f, boundaryLE_embeddingUpIntLE_iff
embeddingUpNat 📖CompOp
4 mathmath: embeddingUpNat_f, instIsRelIffNatIntEmbeddingUpNat, CochainComplex.instIsStrictlyGEExtendNatIntEmbeddingUpNatOfNat, instIsTruncGENatIntEmbeddingUpNat

Theorems

NameKindAssumesProvesValidatesDepends On
embeddingDown'Add_f 📖mathematicalEmbedding.f
down'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingDown'Add
embeddingDownNat_f 📖mathematicalEmbedding.f
down
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
up
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingDownNat
AddRightCancelSemigroup.toIsRightCancelAdd
embeddingUp'Add_f 📖mathematicalEmbedding.f
up'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingUp'Add
embeddingUpIntGE_f 📖mathematicalEmbedding.f
up
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpIntGE
AddRightCancelSemigroup.toIsRightCancelAdd
embeddingUpIntLE_f 📖mathematicalEmbedding.f
down
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
up
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpIntLE
AddRightCancelSemigroup.toIsRightCancelAdd
embeddingUpNat_f 📖mathematicalEmbedding.f
up
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpNat
AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffEmbeddingDown'Add 📖mathematicalEmbedding.IsRelIff
down'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingDown'Add
Embedding.instIsRelIffMk'
instIsRelIffEmbeddingUp'Add 📖mathematicalEmbedding.IsRelIff
up'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingUp'Add
Embedding.instIsRelIffMk'
instIsRelIffNatIntEmbeddingDownNat 📖mathematicalEmbedding.IsRelIff
down
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
up
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingDownNat
AddRightCancelSemigroup.toIsRightCancelAdd
Embedding.instIsRelIffMk'
instIsRelIffNatIntEmbeddingUpIntGE 📖mathematicalEmbedding.IsRelIff
up
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpIntGE
AddRightCancelSemigroup.toIsRightCancelAdd
Embedding.instIsRelIffMk'
instIsRelIffNatIntEmbeddingUpIntLE 📖mathematicalEmbedding.IsRelIff
down
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
up
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpIntLE
AddRightCancelSemigroup.toIsRightCancelAdd
Embedding.instIsRelIffMk'
instIsRelIffNatIntEmbeddingUpNat 📖mathematicalEmbedding.IsRelIff
up
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpNat
AddRightCancelSemigroup.toIsRightCancelAdd
Embedding.instIsRelIffMk'
instIsTruncGEEmbeddingUp'Add 📖mathematicalEmbedding.IsTruncGE
up'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingUp'Add
instIsRelIffEmbeddingUp'Add
add_right_comm
instIsTruncGENatIntEmbeddingUpIntGE 📖mathematicalEmbedding.IsTruncGE
up
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpIntGE
AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffNatIntEmbeddingUpIntGE
instIsTruncGENatIntEmbeddingUpNat 📖mathematicalEmbedding.IsTruncGE
up
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpNat
AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffNatIntEmbeddingUpNat
instIsTruncLEEmbeddingDown'Add 📖mathematicalEmbedding.IsTruncLE
down'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingDown'Add
instIsRelIffEmbeddingDown'Add
add_right_comm
instIsTruncLENatIntEmbeddingDownNat 📖mathematicalEmbedding.IsTruncLE
down
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
up
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingDownNat
AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffNatIntEmbeddingDownNat
instIsTruncLENatIntEmbeddingUpIntLE 📖mathematicalEmbedding.IsTruncLE
down
AddRightCancelSemigroup.toIsRightCancelAdd
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
up
AddGroup.toAddCancelMonoid
Int.instAddGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Int.instRing
embeddingUpIntLE
AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffNatIntEmbeddingUpIntLE
notMem_range_embeddingUpIntGE_iff 📖AddRightCancelSemigroup.toIsRightCancelAdd
notMem_range_embeddingUpIntLE_iff 📖AddRightCancelSemigroup.toIsRightCancelAdd

ComplexShape.Embedding

Definitions

NameCategoryTheorems
IsRelIff 📖CompData
12 mathmath: instIsRelIffMk', ComplexShape.instIsRelIffNatIntEmbeddingUpIntLE, instIsRelIffOp, ComplexShape.instIsRelIffNatIntEmbeddingDownNat, ComplexShape.instIsRelIffNatIntEmbeddingUpIntGE, ComplexShape.instIsRelIffIntEmbeddingDownIntUpInt, ComplexShape.instIsRelIffNatIntEmbeddingUpNat, IsTruncLE.toIsRelIff, ComplexShape.instIsRelIffEmbeddingDown'Add, ComplexShape.instIsRelIffEmbeddingUp'Add, ComplexShape.instIsRelIffIntEmbeddingUpIntDownInt, IsTruncGE.toIsRelIff
IsTruncGE 📖CompData
4 mathmath: ComplexShape.instIsTruncGENatIntEmbeddingUpIntGE, ComplexShape.instIsTruncGEEmbeddingUp'Add, instIsTruncGEOpOfIsTruncLE, ComplexShape.instIsTruncGENatIntEmbeddingUpNat
IsTruncLE 📖CompData
4 mathmath: ComplexShape.instIsTruncLEEmbeddingDown'Add, ComplexShape.instIsTruncLENatIntEmbeddingUpIntLE, instIsTruncLEOpOfIsTruncGE, ComplexShape.instIsTruncLENatIntEmbeddingDownNat
f 📖CompOp
51 mathmath: IsTruncGE.mem_next, ComplexShape.embeddingUpIntDownInt_f, mem_prev, AreComplementary.desc'_inl, ComplexShape.embeddingDown'Add_f, prev_f_of_not_boundaryGE, HomologicalComplex.restriction.sc'Iso_inv_τ₃, op_f, CochainComplex.homotopyUnop_hom_eq, HomologicalComplex.instQuasiIsoAtιTruncLEF, HomologicalComplex.restriction.sc'Iso_inv_τ₁, AreComplementary.desc_inr, HomologicalComplex.restriction_X, injective_f, ComplexShape.embeddingUpNat_f, AreComplementary.desc_inl, AreComplementary.exists_i₁, HomologicalComplex.restriction_d, ComplexShape.embeddingUp'Add_f, HomologicalComplex.restriction.sc'Iso_hom_τ₂, IsTruncLE.mem_prev, AreComplementary.exists_i₂, AreComplementary.union, HomologicalComplex.IsSupportedOutside.exactAt, AreComplementary.equiv_inl, prev_f, CochainComplex.homotopyOp_hom_eq, Homotopy.ofExtend_hom, HomologicalComplex.IsStrictlySupportedOutside.isZero, homRestrict.comm_assoc, f_eq_of_r_eq_some, homRestrict.comm, ComplexShape.embeddingUpIntLE_f, HomologicalComplex.extend.instHasHomologyF, ComplexShape.embeddingDownNat_f, HomologicalComplex.restrictionMap_f, HomologicalComplex.restriction.sc'Iso_inv_τ₂, next_f, mem_next, next_f_of_not_boundaryLE, AreComplementary.equiv_inr, ComplexShape.embeddingDownIntUpInt_f, ComplexShape.embeddingUpIntGE_f, mk'_f, HomologicalComplex.restriction.sc'Iso_hom_τ₃, HomologicalComplex.instQuasiIsoAtπTruncGEF, rel_iff, HomologicalComplex.restriction.sc'Iso_hom_τ₁, r_f, rel, AreComplementary.desc'_inr
mk' 📖CompOp
2 mathmath: instIsRelIffMk', mk'_f
op 📖CompOp
13 mathmath: op_f, HomologicalComplex.extend_op_d_assoc, HomologicalComplex.isStrictlySupportedOutside_op_iff, instIsRelIffOp, instIsTruncLEOpOfIsTruncGE, HomologicalComplex.isSupportedOutside_op_iff, HomologicalComplex.extend_op_d, HomologicalComplex.isStrictlySupported_op_iff, op_boundaryLE_iff, op_boundaryGE_iff, instIsTruncGEOpOfIsTruncLE, HomologicalComplex.isSupported_op_iff, HomologicalComplex.instIsStrictlySupportedOppositeOpOp
r 📖CompOp
3 mathmath: r_eq_some, r_eq_none, r_f

Theorems

NameKindAssumesProvesValidatesDepends On
f_eq_of_r_eq_some 📖mathematicalrfr_f
r_eq_none
injective_f 📖mathematicalf
instIsRelIffMk' 📖mathematicalComplexShape.RelIsRelIff
mk'
instIsRelIffOp 📖mathematicalIsRelIff
ComplexShape.symm
op
rel_iff
instIsTruncGEOpOfIsTruncLE 📖mathematicalIsTruncGE
ComplexShape.symm
op
instIsRelIffOp
IsTruncLE.toIsRelIff
mem_prev
instIsTruncLEOpOfIsTruncGE 📖mathematicalIsTruncLE
ComplexShape.symm
op
instIsRelIffOp
IsTruncGE.toIsRelIff
mem_next
mem_next 📖mathematicalComplexShape.Rel
f
fIsTruncGE.mem_next
mem_prev 📖mathematicalComplexShape.Rel
f
fIsTruncLE.mem_prev
mk'_f 📖mathematicalComplexShape.Relf
mk'
op_f 📖mathematicalf
ComplexShape.symm
op
r_eq_none 📖mathematicalr
r_eq_some 📖mathematicalfrinjective_f
r_f 📖mathematicalr
f
r_eq_some
rel 📖mathematicalComplexShape.RelComplexShape.Rel
f
rel_iff 📖mathematicalComplexShape.Rel
f
IsRelIff.rel'
rel

ComplexShape.Embedding.IsRelIff

Theorems

NameKindAssumesProvesValidatesDepends On
rel' 📖mathematicalComplexShape.Rel
ComplexShape.Embedding.f
ComplexShape.Rel

ComplexShape.Embedding.IsTruncGE

Theorems

NameKindAssumesProvesValidatesDepends On
mem_next 📖mathematicalComplexShape.Rel
ComplexShape.Embedding.f
ComplexShape.Embedding.f
toIsRelIff 📖mathematicalComplexShape.Embedding.IsRelIff

ComplexShape.Embedding.IsTruncLE

Theorems

NameKindAssumesProvesValidatesDepends On
mem_prev 📖mathematicalComplexShape.Rel
ComplexShape.Embedding.f
ComplexShape.Embedding.f
toIsRelIff 📖mathematicalComplexShape.Embedding.IsRelIff

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