Documentation Verification Report

Basic

๐Ÿ“ 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 ๐Ÿ“–CompOp
3 mathmath: instIsTruncLEEmbeddingDown'Add, embeddingDown'Add_f, instIsRelIffEmbeddingDown'Add
embeddingDownNat ๐Ÿ“–CompOp
4 mathmath: CochainComplex.instIsStrictlyLEExtendNatIntEmbeddingDownNatOfNat, instIsRelIffNatIntEmbeddingDownNat, embeddingDownNat_f, instIsTruncLENatIntEmbeddingDownNat
embeddingUp'Add ๐Ÿ“–CompOp
3 mathmath: embeddingUp'Add_f, instIsTruncGEEmbeddingUp'Add, instIsRelIffEmbeddingUp'Add
embeddingUpIntGE ๐Ÿ“–CompOp
10 mathmath: Embedding.embeddingUpInt_areComplementary, instIsTruncGENatIntEmbeddingUpIntGE, CochainComplex.quasiIso_truncGEMap_iff, instIsRelIffNatIntEmbeddingUpIntGE, boundaryGE_embeddingUpIntGE_iff, CochainComplex.quasiIso_ฯ€TruncGE_iff, CochainComplex.ConnectData.restrictionGEIso_inv_f, embeddingUpIntGE_f, CochainComplex.instQuasiIsoIntฯ€TruncGEOfIsGE, CochainComplex.ConnectData.restrictionGEIso_hom_f
embeddingUpIntLE ๐Ÿ“–CompOp
10 mathmath: CochainComplex.quasiIso_truncLEMap_iff, instIsTruncLENatIntEmbeddingUpIntLE, instIsRelIffNatIntEmbeddingUpIntLE, Embedding.embeddingUpInt_areComplementary, CochainComplex.ConnectData.restrictionLEIso_inv_f, CochainComplex.instQuasiIsoIntฮนTruncLEOfIsLE, CochainComplex.ConnectData.restrictionLEIso_hom_f, CochainComplex.quasiIso_ฮนTruncLE_iff, embeddingUpIntLE_f, boundaryLE_embeddingUpIntLE_iff
embeddingUpNat ๐Ÿ“–CompOp
4 mathmath: embeddingUpNat_f, instIsRelIffNatIntEmbeddingUpNat, CochainComplex.instIsStrictlyGEExtendNatIntEmbeddingUpNatOfNat, instIsTruncGENatIntEmbeddingUpNat

Theorems

NameKindAssumesProvesValidatesDepends On
embeddingDown'Add_f ๐Ÿ“–mathematicalโ€”Embedding.f
down'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingDown'Add
โ€”โ€”
embeddingDownNat_f ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
embeddingUp'Add_f ๐Ÿ“–mathematicalโ€”Embedding.f
up'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingUp'Add
โ€”โ€”
embeddingUpIntGE_f ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
embeddingUpIntLE_f ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
embeddingUpNat_f ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffEmbeddingDown'Add ๐Ÿ“–mathematicalโ€”Embedding.IsRelIff
down'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingDown'Add
โ€”Embedding.instIsRelIffMk'
instIsRelIffEmbeddingUp'Add ๐Ÿ“–mathematicalโ€”Embedding.IsRelIff
up'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingUp'Add
โ€”Embedding.instIsRelIffMk'
instIsRelIffNatIntEmbeddingDownNat ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
Embedding.instIsRelIffMk'
instIsRelIffNatIntEmbeddingUpIntGE ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
Embedding.instIsRelIffMk'
instIsRelIffNatIntEmbeddingUpIntLE ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
Embedding.instIsRelIffMk'
instIsRelIffNatIntEmbeddingUpNat ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
Embedding.instIsRelIffMk'
instIsTruncGEEmbeddingUp'Add ๐Ÿ“–mathematicalโ€”Embedding.IsTruncGE
up'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingUp'Add
โ€”instIsRelIffEmbeddingUp'Add
add_right_comm
instIsTruncGENatIntEmbeddingUpIntGE ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffNatIntEmbeddingUpIntGE
instIsTruncGENatIntEmbeddingUpNat ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffNatIntEmbeddingUpNat
instIsTruncLEEmbeddingDown'Add ๐Ÿ“–mathematicalโ€”Embedding.IsTruncLE
down'
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
embeddingDown'Add
โ€”instIsRelIffEmbeddingDown'Add
add_right_comm
instIsTruncLENatIntEmbeddingDownNat ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffNatIntEmbeddingDownNat
instIsTruncLENatIntEmbeddingUpIntLE ๐Ÿ“–mathematicalโ€”Embedding.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
โ€”AddRightCancelSemigroup.toIsRightCancelAdd
instIsRelIffNatIntEmbeddingUpIntLE
notMem_range_embeddingUpIntGE_iff ๐Ÿ“–โ€”โ€”โ€”โ€”AddRightCancelSemigroup.toIsRightCancelAdd
notMem_range_embeddingUpIntLE_iff ๐Ÿ“–โ€”โ€”โ€”โ€”AddRightCancelSemigroup.toIsRightCancelAdd

ComplexShape.Embedding

Definitions

NameCategoryTheorems
IsRelIff ๐Ÿ“–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 ๐Ÿ“–CompData
4 mathmath: ComplexShape.instIsTruncGENatIntEmbeddingUpIntGE, ComplexShape.instIsTruncGEEmbeddingUp'Add, instIsTruncGEOpOfIsTruncLE, ComplexShape.instIsTruncGENatIntEmbeddingUpNat
IsTruncLE ๐Ÿ“–CompData
4 mathmath: ComplexShape.instIsTruncLEEmbeddingDown'Add, ComplexShape.instIsTruncLENatIntEmbeddingUpIntLE, instIsTruncLEOpOfIsTruncGE, ComplexShape.instIsTruncLENatIntEmbeddingDownNat
f ๐Ÿ“–CompOp
41 mathmath: ComplexShape.embeddingUpIntDownInt_f, AreComplementary.desc'_inl, ComplexShape.embeddingDown'Add_f, prev_f_of_not_boundaryGE, op_f, CochainComplex.homotopyUnop_hom_eq, HomologicalComplex.instQuasiIsoAtฮนTruncLEF, AreComplementary.desc_inr, HomologicalComplex.restriction_X, injective_f, ComplexShape.embeddingUpNat_f, AreComplementary.desc_inl, AreComplementary.exists_iโ‚, HomologicalComplex.restriction_d, ComplexShape.embeddingUp'Add_f, AreComplementary.exists_iโ‚‚, 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, next_f, next_f_of_not_boundaryLE, AreComplementary.equiv_inr, ComplexShape.embeddingDownIntUpInt_f, ComplexShape.embeddingUpIntGE_f, mk'_f, HomologicalComplex.instQuasiIsoAtฯ€TruncGEF, rel_iff, r_f, rel, AreComplementary.desc'_inr
mk' ๐Ÿ“–CompOp
2 mathmath: instIsRelIffMk', mk'_f
op ๐Ÿ“–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 ๐Ÿ“–CompOp
3 mathmath: r_eq_some, r_eq_none, r_f

Theorems

NameKindAssumesProvesValidatesDepends On
f_eq_of_r_eq_some ๐Ÿ“–mathematicalrfโ€”r_f
r_eq_none
injective_f ๐Ÿ“–mathematicalโ€”fโ€”โ€”
instIsRelIffMk' ๐Ÿ“–mathematicalComplexShape.RelIsRelIff
mk'
โ€”โ€”
instIsRelIffOp ๐Ÿ“–mathematicalโ€”IsRelIff
ComplexShape.symm
op
โ€”rel_iff
instIsTruncGEOpOfIsTruncLE ๐Ÿ“–mathematicalโ€”IsTruncGE
ComplexShape.symm
op
โ€”instIsRelIffOp
IsTruncLE.toIsRelIff
mem_prev
instIsTruncLEOpOfIsTruncGE ๐Ÿ“–mathematicalโ€”IsTruncLE
ComplexShape.symm
op
โ€”instIsRelIffOp
IsTruncGE.toIsRelIff
mem_next
mem_next ๐Ÿ“–โ€”ComplexShape.Rel
f
โ€”โ€”IsTruncGE.mem_next
mem_prev ๐Ÿ“–โ€”ComplexShape.Rel
f
โ€”โ€”IsTruncLE.mem_prev
mk'_f ๐Ÿ“–mathematicalComplexShape.Relf
mk'
โ€”โ€”
op_f ๐Ÿ“–mathematicalโ€”f
ComplexShape.symm
op
โ€”โ€”
r_eq_none ๐Ÿ“–mathematicalโ€”rโ€”โ€”
r_eq_some ๐Ÿ“–mathematicalfrโ€”injective_f
r_f ๐Ÿ“–mathematicalโ€”r
f
โ€”r_eq_some
rel ๐Ÿ“–mathematicalComplexShape.Relfโ€”โ€”
rel_iff ๐Ÿ“–mathematicalโ€”ComplexShape.Rel
f
โ€”IsRelIff.rel'
rel

ComplexShape.Embedding.IsRelIff

Theorems

NameKindAssumesProvesValidatesDepends On
rel' ๐Ÿ“–โ€”ComplexShape.Rel
ComplexShape.Embedding.f
โ€”โ€”โ€”

ComplexShape.Embedding.IsTruncGE

Theorems

NameKindAssumesProvesValidatesDepends On
mem_next ๐Ÿ“–โ€”ComplexShape.Rel
ComplexShape.Embedding.f
โ€”โ€”โ€”
toIsRelIff ๐Ÿ“–mathematicalโ€”ComplexShape.Embedding.IsRelIffโ€”โ€”

ComplexShape.Embedding.IsTruncLE

Theorems

NameKindAssumesProvesValidatesDepends On
mem_prev ๐Ÿ“–โ€”ComplexShape.Rel
ComplexShape.Embedding.f
โ€”โ€”โ€”
toIsRelIff ๐Ÿ“–mathematicalโ€”ComplexShape.Embedding.IsRelIffโ€”โ€”

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