Documentation Verification Report

Between

πŸ“ Source: Mathlib/Analysis/Convex/Between.lean

Statistics

MetricCount
DefinitionsSbtw, Wbtw, affineSegment
3
TheoremsclosedInterior_eq_affineSegment, closedInterior_face_eq_affineSegment, interior_eq_image_Ioo, mem_closedInterior_face_iff_wbtw, mem_closedInterior_iff_wbtw, mem_interior_face_iff_sbtw, mem_interior_iff_sbtw, sbtw_map_iff, wbtw_map_iff, not_wbtw_of_injective, mem_of_wbtw, right_mem_of_wbtw, wbtw_or_wbtw_or_wbtw, mem_of_wbtw, sbtw_map_iff, wbtw_map_iff, add_const, affineCombination_of_mem_affineSpan_pair, const_add, const_sub, const_vadd, const_vsub, left_mem_affineSpan, left_mem_image_Ioi, left_ne, left_ne_right, mem_image_Ioo, ne_left, ne_right, neg, not_rotate, not_swap_left, not_swap_right, of_lt_of_lt, right_mem_affineSpan, right_mem_image_Ioi, right_ne, sub_const, trans_expand_left, trans_expand_right, trans_left, trans_left_right, trans_right, trans_right_left, trans_wbtw_left_ne, trans_wbtw_right_ne, vadd_const, vsub_const, wbtw, sbtw_map_iff, wbtw_map_iff, add_const, collinear, const_add, const_sub, const_vadd, const_vsub, left_mem_affineSpan_of_right_ne, left_mem_image_Ici_of_right_ne, left_ne_right_of_ne_left, left_ne_right_of_ne_right, map, mem_affineSpan, mem_segment, neg, of_le_of_le, right_mem_affineSpan_of_left_ne, right_mem_image_Ici_of_left_ne, rotate_iff, sameRay_vsub, sameRay_vsub_left, sameRay_vsub_right, sub_const, swap_left_iff, swap_right_iff, trans_expand_left, trans_expand_right, trans_left, trans_left_ne, trans_left_right, trans_right, trans_right_left, trans_right_ne, trans_sbtw_left, trans_sbtw_right, vadd_const, vsub_const, affineSegment_comm, affineSegment_const_vadd_image, affineSegment_const_vsub_image, affineSegment_eq_segment, affineSegment_image, affineSegment_same, affineSegment_subset_affineSpan, affineSegment_vadd_const_image, affineSegment_vsub_const_image, left_mem_affineSegment, mem_const_vadd_affineSegment, mem_const_vsub_affineSegment, mem_segment_iff_wbtw, mem_vadd_const_affineSegment, mem_vsub_const_affineSegment, not_sbtw_self, not_sbtw_self_left, not_sbtw_self_right, right_mem_affineSegment, sbtw_add_const_iff, sbtw_comm, sbtw_const_add_iff, sbtw_const_sub_iff, sbtw_const_vadd_iff, sbtw_const_vsub_iff, sbtw_iff_left_ne_and_right_mem_image_Ioi, sbtw_iff_mem_image_Ioo_and_ne, sbtw_iff_right_ne_and_left_mem_image_Ioi, sbtw_lineMap_iff, sbtw_midpoint_of_ne, sbtw_mul_sub_add_iff, sbtw_neg_iff, sbtw_of_sbtw_of_sbtw_of_mem_affineSpan_pair, sbtw_one_zero_iff, sbtw_pointReflection_of_ne, sbtw_sub_const_iff, sbtw_vadd_const_iff, sbtw_vsub_const_iff, sbtw_zero_one_iff, wbtw_add_const_iff, wbtw_comm, wbtw_const_add_iff, wbtw_const_sub_iff, wbtw_const_vadd_iff, wbtw_const_vsub_iff, wbtw_iff_left_eq_or_right_mem_image_Ici, wbtw_iff_of_le, wbtw_iff_right_eq_or_left_mem_image_Ici, wbtw_iff_sameRay_vsub, wbtw_lineMap_iff, wbtw_midpoint, wbtw_mul_sub_add_iff, wbtw_neg_iff, wbtw_one_zero_iff, wbtw_or_wbtw_smul_vadd_of_nonneg, wbtw_or_wbtw_smul_vadd_of_nonpos, wbtw_pointReflection, wbtw_rotate_iff, wbtw_self_iff, wbtw_self_left, wbtw_self_right, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, wbtw_sub_const_iff, wbtw_swap_left_iff, wbtw_swap_right_iff, wbtw_total_of_sameRay_vsub_left, wbtw_vadd_const_iff, wbtw_vsub_const_iff, wbtw_zero_one_iff
159
Total162

Affine.Simplex

Theorems

NameKindAssumesProvesValidatesDepends On
closedInterior_eq_affineSegment πŸ“–mathematicalβ€”closedInterior
affineSegment
points
β€”Set.ext
Fintype.complete
Finset.affineCombinationLineMapWeights_apply_left
Fin.instNeZeroHAddNatOfNat_mathlib_1
Fin.sum_univ_two
add_sub_cancel_right
Finset.affineCombinationLineMapWeights_apply_right
Finset.affineCombination_affineCombinationLineMapWeights
Finset.mem_univ
Set.mem_image_of_mem
affineCombination_mem_closedInterior_iff
Finset.sum_affineCombinationLineMapWeights
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
AddGroup.toOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedCancelAddMonoid.toAddLeftReflectLT
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
closedInterior_face_eq_affineSegment πŸ“–mathematicalβ€”closedInterior
face
Finset
Finset.instInsert
Finset.instSingleton
Finset.card_pair
affineSegment
points
β€”Ne.lt_or_gt
min_eq_left
LT.lt.le
max_eq_right
affineSegment_comm
max_eq_left
min_eq_right
Finset.card_pair
closedInterior_eq_affineSegment
face_points
Finset.card_pos
Finset.insert_nonempty
Finset.min'_pair
Finset.orderEmbOfFin_zero
Finset.max'_pair
Finset.orderEmbOfFin_last
interior_eq_image_Ioo πŸ“–mathematicalβ€”interior
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
points
Set.Ioo
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”Set.ext
Fintype.complete
Finset.affineCombinationLineMapWeights_apply_left
Fin.instNeZeroHAddNatOfNat_mathlib_1
Fin.sum_univ_two
add_sub_cancel_right
Finset.affineCombinationLineMapWeights_apply_right
Finset.affineCombination_affineCombinationLineMapWeights
Finset.mem_univ
Set.mem_image_of_mem
affineCombination_mem_interior_iff
Finset.sum_affineCombinationLineMapWeights
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
mem_closedInterior_face_iff_wbtw πŸ“–mathematicalβ€”Set
Set.instMembership
closedInterior
face
Finset
Finset.instInsert
Finset.instSingleton
Finset.card_pair
Wbtw
points
β€”Finset.card_pair
closedInterior_face_eq_affineSegment
Wbtw.eq_1
mem_closedInterior_iff_wbtw πŸ“–mathematicalβ€”Set
Set.instMembership
closedInterior
Wbtw
points
β€”closedInterior_eq_affineSegment
Wbtw.eq_1
mem_interior_face_iff_sbtw πŸ“–mathematicalβ€”Set
Set.instMembership
interior
face
Finset
Finset.instInsert
Finset.instSingleton
Finset.card_pair
Sbtw
points
β€”Ne.lt_or_gt
min_eq_left
LT.lt.le
max_eq_right
sbtw_comm
max_eq_left
min_eq_right
Finset.card_pair
mem_interior_iff_sbtw
face_points
Finset.card_pos
Finset.insert_nonempty
Finset.min'_pair
Finset.orderEmbOfFin_zero
Finset.max'_pair
Finset.orderEmbOfFin_last
mem_interior_iff_sbtw πŸ“–mathematicalβ€”Set
Set.instMembership
interior
Sbtw
points
β€”interior_eq_image_Ioo
sbtw_iff_mem_image_Ioo_and_ne
AffineIndependent.injective
IsDomain.toNontrivial
independent

AffineEquiv

Theorems

NameKindAssumesProvesValidatesDepends On
sbtw_map_iff πŸ“–mathematicalβ€”Sbtw
DFunLike.coe
AffineEquiv
EquivLike.toFunLike
equivLike
β€”injective
Function.Injective.sbtw_map_iff
wbtw_map_iff πŸ“–mathematicalβ€”Wbtw
DFunLike.coe
AffineEquiv
EquivLike.toFunLike
equivLike
β€”injective
Function.Injective.wbtw_map_iff

AffineIndependent

Theorems

NameKindAssumesProvesValidatesDepends On
not_wbtw_of_injective πŸ“–mathematicalMatrix.vecCons
Matrix.vecEmpty
AffineIndependent
DivisionRing.toRing
Field.toDivisionRing
Wbtw
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”comp_embedding
Mathlib.Tactic.Contrapose.contraposeβ‚„
Set.range_comp
Matrix.range_cons
Matrix.range_empty
Set.union_empty
Set.union_singleton
Set.union_insert
Set.image_insert_eq
Set.image_singleton
Wbtw.collinear
Wbtw.symm
IsStrictOrderedRing.toIsOrderedRing
affineIndependent_iff_not_collinear

AffineSubspace

Theorems

NameKindAssumesProvesValidatesDepends On
mem_of_wbtw πŸ“–β€”Wbtw
AffineSubspace
SetLike.instMembership
instSetLike
β€”β€”AffineMap.lineMap_mem
right_mem_of_wbtw πŸ“–β€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AffineSubspace
SetLike.instMembership
instSetLike
β€”β€”AffineMap.lineMap_apply_zero
AffineMap.lineMap_lineMap_right
inv_mul_cancelβ‚€
AffineMap.lineMap_apply_one
AffineMap.lineMap_mem

Collinear

Theorems

NameKindAssumesProvesValidatesDepends On
wbtw_or_wbtw_or_wbtw πŸ“–mathematicalCollinear
Field.toDivisionRing
Set
Set.instInsert
Set.instSingletonSet
Wbtw
DivisionRing.toRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”collinear_iff_of_mem
Set.mem_insert
lt_trichotomy
wbtw_comm
IsStrictOrderedRing.toIsOrderedRing
wbtw_or_wbtw_smul_vadd_of_nonpos
LT.lt.le
zero_smul
zero_vadd
wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos
wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg
wbtw_or_wbtw_smul_vadd_of_nonneg

Convex

Theorems

NameKindAssumesProvesValidatesDepends On
mem_of_wbtw πŸ“–β€”Convex
Ring.toSemiring
AddCommGroup.toAddCommMonoid
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Wbtw
addGroupIsAddTorsor
Set
Set.instMembership
β€”β€”segment_subset
Wbtw.mem_segment

Function.Injective

Theorems

NameKindAssumesProvesValidatesDepends On
sbtw_map_iff πŸ“–mathematicalDFunLike.coe
AffineMap
AffineMap.instFunLike
Sbtwβ€”wbtw_map_iff
wbtw_map_iff πŸ“–mathematicalDFunLike.coe
AffineMap
AffineMap.instFunLike
Wbtwβ€”mem_set_image
affineSegment_image
Wbtw.eq_1
Wbtw.map

Sbtw

Theorems

NameKindAssumesProvesValidatesDepends On
add_const πŸ“–mathematicalSbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
β€”sbtw_add_const_iff
affineCombination_of_mem_affineSpan_pair πŸ“–β€”AffineIndependent
Finset.sum
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
AffineSubspace
SetLike.instMembership
AffineSubspace.instSetLike
affineSpan
Set
Set.instInsert
DFunLike.coe
AffineMap
Pi.addCommGroup
Ring.toAddCommGroup
Pi.Function.module
Ring.toSemiring
NonUnitalSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonUnitalSemiring
Semiring.toModule
Finset.instAddTorsorForall
AffineMap.instFunLike
Finset.affineCombination
Set.instSingletonSet
Finset
Finset.instMembership
Sbtw
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
β€”β€”affineCombination_mem_affineSpan_pair
Finset.affineCombination_congr
Finset.weightedVSub_vadd_affineCombination
Finset.weightedVSub_const_smul
Finset.affineCombination_vsub
AffineMap.lineMap_apply
sbtw_lineMap_iff
sbtw_mul_sub_add_iff
vsub_ne_zero
Finset.sum_congr
Finset.sum_sub_distrib
sub_self
sub_eq_zero
Pi.sub_apply
const_add πŸ“–mathematicalSbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
β€”sbtw_const_add_iff
const_sub πŸ“–mathematicalSbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
β€”sbtw_const_sub_iff
const_vadd πŸ“–mathematicalSbtwHVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
β€”sbtw_const_vadd_iff
const_vsub πŸ“–mathematicalSbtwaddGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”sbtw_const_vsub_iff
left_mem_affineSpan πŸ“–mathematicalSbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AffineSubspace
SetLike.instMembership
AffineSubspace.instSetLike
affineSpan
Set
Set.instInsert
Set.instSingletonSet
β€”right_mem_affineSpan
symm
IsStrictOrderedRing.toIsOrderedRing
left_mem_image_Ioi πŸ“–mathematicalSbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ioi
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”right_mem_image_Ioi
symm
IsStrictOrderedRing.toIsOrderedRing
left_ne πŸ“–β€”Sbtwβ€”β€”β€”
left_ne_right πŸ“–β€”Sbtwβ€”β€”Wbtw.left_ne_right_of_ne_left
wbtw
mem_image_Ioo πŸ“–mathematicalSbtwSet
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ioo
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”Set.eq_endpoints_or_mem_Ioo_of_mem_Icc
AffineMap.lineMap_apply_zero
AffineMap.lineMap_apply_one
ne_left πŸ“–β€”Sbtwβ€”β€”β€”
ne_right πŸ“–β€”Sbtwβ€”β€”β€”
neg πŸ“–mathematicalSbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”sbtw_neg_iff
not_rotate πŸ“–mathematicalSbtwWbtwβ€”left_ne
Wbtw.rotate_iff
wbtw
not_swap_left πŸ“–mathematicalSbtwWbtwβ€”left_ne
Wbtw.swap_left_iff
wbtw
not_swap_right πŸ“–mathematicalSbtwWbtwβ€”ne_right
Wbtw.swap_right_iff
wbtw
of_lt_of_lt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Sbtw
DivisionRing.toRing
Field.toDivisionRing
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
β€”Wbtw.of_le_of_le
LT.lt.le
LT.lt.ne'
LT.lt.ne
right_mem_affineSpan πŸ“–mathematicalSbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AffineSubspace
SetLike.instMembership
AffineSubspace.instSetLike
affineSpan
Set
Set.instInsert
Set.instSingletonSet
β€”Wbtw.right_mem_affineSpan_of_left_ne
wbtw
left_ne
right_mem_image_Ioi πŸ“–mathematicalSbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ioi
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”sbtw_iff_left_ne_and_right_mem_image_Ioi
right_ne πŸ“–β€”Sbtwβ€”β€”β€”
sub_const πŸ“–mathematicalSbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
β€”sbtw_sub_const_iff
trans_expand_left πŸ“–β€”Sbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”Wbtw.trans_expand_left
wbtw
left_ne
left_ne_right
IsStrictOrderedRing.toIsOrderedRing
trans_expand_right πŸ“–β€”Sbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”trans_right
IsStrictOrderedRing.toIsOrderedRing
instIsDomain
instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors
GroupWithZero.toNoZeroSMulDivisors
trans_expand_left
trans_left πŸ“–β€”Sbtwβ€”β€”Wbtw.trans_sbtw_left
wbtw
trans_left_right πŸ“–β€”Sbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”Wbtw.trans_left_right
wbtw
right_ne
ne_right
trans_right πŸ“–β€”Sbtwβ€”β€”Wbtw.trans_sbtw_right
wbtw
trans_right_left πŸ“–β€”Sbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”Wbtw.trans_right_left
wbtw
ne_left
left_ne
trans_wbtw_left_ne πŸ“–β€”Sbtw
Wbtw
β€”β€”Wbtw.trans_left_ne
wbtw
ne_right
trans_wbtw_right_ne πŸ“–β€”Sbtw
Wbtw
β€”β€”Wbtw.trans_right_ne
wbtw
left_ne
vadd_const πŸ“–mathematicalSbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
β€”sbtw_vadd_const_iff
vsub_const πŸ“–mathematicalSbtwaddGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”sbtw_vsub_const_iff
wbtw πŸ“–mathematicalSbtwWbtwβ€”β€”

Set.InjOn

Theorems

NameKindAssumesProvesValidatesDepends On
sbtw_map_iff πŸ“–mathematicalSet.InjOn
DFunLike.coe
AffineMap
AffineMap.instFunLike
SetLike.coe
AffineSubspace
AffineSubspace.instSetLike
SetLike.instMembership
Sbtwβ€”wbtw_map_iff
ne_iff
wbtw_map_iff πŸ“–mathematicalSet.InjOn
DFunLike.coe
AffineMap
AffineMap.instFunLike
SetLike.coe
AffineSubspace
AffineSubspace.instSetLike
SetLike.instMembership
Wbtwβ€”mem_image_iff
HasSubset.Subset.trans
Set.instIsTransSubset
affineSegment_subset_affineSpan
affineSpan_le
Set.pair_subset
affineSegment_image
Wbtw.eq_1
Wbtw.map

Wbtw

Theorems

NameKindAssumesProvesValidatesDepends On
add_const πŸ“–mathematicalWbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
β€”wbtw_add_const_iff
collinear πŸ“–mathematicalWbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Collinear
Set
Set.instInsert
Set.instSingletonSet
β€”collinear_iff_exists_forall_eq_smul_vadd
zero_smul
zero_vadd
one_smul
vsub_vadd
const_add πŸ“–mathematicalWbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
β€”wbtw_const_add_iff
const_sub πŸ“–mathematicalWbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
β€”wbtw_const_sub_iff
const_vadd πŸ“–mathematicalWbtwHVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
β€”wbtw_const_vadd_iff
const_vsub πŸ“–mathematicalWbtwaddGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”wbtw_const_vsub_iff
left_mem_affineSpan_of_right_ne πŸ“–mathematicalWbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AffineSubspace
SetLike.instMembership
AffineSubspace.instSetLike
affineSpan
Set
Set.instInsert
Set.instSingletonSet
β€”right_mem_affineSpan_of_left_ne
symm
IsStrictOrderedRing.toIsOrderedRing
left_mem_image_Ici_of_right_ne πŸ“–mathematicalWbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ici
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”right_mem_image_Ici_of_left_ne
symm
IsStrictOrderedRing.toIsOrderedRing
left_ne_right_of_ne_left πŸ“–β€”Wbtwβ€”β€”wbtw_self_iff
left_ne_right_of_ne_right πŸ“–β€”Wbtwβ€”β€”wbtw_self_iff
map πŸ“–mathematicalWbtwDFunLike.coe
AffineMap
AffineMap.instFunLike
β€”eq_1
affineSegment_image
Set.mem_image_of_mem
mem_affineSpan πŸ“–mathematicalWbtwAffineSubspace
SetLike.instMembership
AffineSubspace.instSetLike
affineSpan
Set
Set.instInsert
Set.instSingletonSet
β€”AffineMap.lineMap_mem_affineSpan_pair
mem_segment πŸ“–mathematicalWbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
Set
Set.instMembership
segment
Ring.toSemiring
AddCommGroup.toAddCommMonoid
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”mem_segment_iff_wbtw
neg πŸ“–mathematicalWbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”wbtw_neg_iff
of_le_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Wbtw
DivisionRing.toRing
Field.toDivisionRing
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
β€”wbtw_iff_of_le
LE.le.trans
right_mem_affineSpan_of_left_ne πŸ“–mathematicalWbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AffineSubspace
SetLike.instMembership
AffineSubspace.instSetLike
affineSpan
Set
Set.instInsert
Set.instSingletonSet
β€”right_mem_image_Ici_of_left_ne
AffineMap.lineMap_mem_affineSpan_pair
right_mem_image_Ici_of_left_ne πŸ“–mathematicalWbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ici
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”wbtw_iff_left_eq_or_right_mem_image_Ici
rotate_iff πŸ“–β€”Wbtwβ€”β€”wbtw_rotate_iff
sameRay_vsub πŸ“–mathematicalWbtw
CommRing.toRing
SameRay
CommRing.toCommSemiring
AddCommGroup.toAddCommMonoid
VSub.vsub
AddTorsor.toVSub
AddCommGroup.toAddGroup
β€”LE.le.lt_or_eq
sub_pos
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
vadd_vsub
smul_smul
vsub_vadd_eq_vsub_sub
smul_sub
Nat.instAtLeastTwoHAddOfNat
Mathlib.Tactic.Ring.mul_congr
Mathlib.Tactic.Ring.sub_congr
Mathlib.Tactic.Ring.cast_pos
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
Mathlib.Tactic.Ring.atom_pf
Mathlib.Tactic.Ring.sub_pf
Mathlib.Tactic.Ring.neg_add
Mathlib.Tactic.Ring.neg_mul
Mathlib.Tactic.Ring.neg_one_mul
Mathlib.Meta.NormNum.IsInt.to_raw_eq
Mathlib.Meta.NormNum.isInt_mul
Mathlib.Meta.NormNum.IsInt.of_raw
Mathlib.Meta.NormNum.IsNat.to_isInt
Mathlib.Meta.NormNum.IsNat.of_raw
Mathlib.Tactic.Ring.neg_zero
Mathlib.Tactic.Ring.add_pf_add_lt
Mathlib.Tactic.Ring.add_pf_zero_add
Mathlib.Tactic.Ring.add_mul
Mathlib.Tactic.Ring.mul_add
Mathlib.Tactic.Ring.mul_pf_right
Mathlib.Tactic.Ring.one_mul
Mathlib.Tactic.Ring.mul_zero
Mathlib.Tactic.Ring.add_pf_add_zero
Mathlib.Tactic.Ring.mul_pp_pf_overlap
Mathlib.Meta.NormNum.IsNat.to_raw_eq
Mathlib.Meta.NormNum.isNat_add
Mathlib.Tactic.Ring.mul_one
Mathlib.Tactic.Ring.zero_mul
Mathlib.Tactic.RingNF.nat_rawCast_1
pow_one
mul_one
Mathlib.Tactic.RingNF.int_rawCast_neg
Mathlib.Tactic.RingNF.mul_neg
add_zero
Mathlib.Tactic.RingNF.add_neg
SameRay.congr_simp
one_smul
vsub_vadd
vsub_self
zero_smul
zero_vadd
sameRay_vsub_left πŸ“–mathematicalWbtw
CommRing.toRing
SameRay
CommRing.toCommSemiring
AddCommGroup.toAddCommMonoid
VSub.vsub
AddTorsor.toVSub
AddCommGroup.toAddGroup
β€”SameRay.congr_simp
vadd_vsub
SameRay.sameRay_nonneg_smul_left
PosSMulMono.toSMulPosMono
IsStrictOrderedRing.toIsOrderedRing
IsOrderedRing.toIsOrderedAddMonoid
IsOrderedModule.toPosSMulMono
IsStrictOrderedModule.toIsOrderedModule
IsStrictOrderedRing.toIsStrictOrderedModule
IsScalarTower.left
sameRay_vsub_right πŸ“–mathematicalWbtw
CommRing.toRing
SameRay
CommRing.toCommSemiring
AddCommGroup.toAddCommMonoid
VSub.vsub
AddTorsor.toVSub
AddCommGroup.toAddGroup
β€”SameRay.congr_simp
vsub_vadd_eq_vsub_sub
sub_smul
one_smul
SameRay.sameRay_nonneg_smul_right
PosSMulMono.toSMulPosMono
IsStrictOrderedRing.toIsOrderedRing
IsOrderedRing.toIsOrderedAddMonoid
IsOrderedModule.toPosSMulMono
IsStrictOrderedModule.toIsOrderedModule
IsStrictOrderedRing.toIsStrictOrderedModule
IsScalarTower.left
sub_nonneg
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
sub_const πŸ“–mathematicalWbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
β€”wbtw_sub_const_iff
swap_left_iff πŸ“–β€”Wbtwβ€”β€”wbtw_swap_left_iff
swap_right_iff πŸ“–β€”Wbtwβ€”β€”wbtw_swap_right_iff
trans_expand_left πŸ“–β€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”div_nonneg
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
mul_nonneg
IsOrderedRing.toPosMulMono
IsStrictOrderedRing.toIsOrderedRing
le_of_not_gt
Mathlib.Tactic.Linarith.lt_irrefl
Mathlib.Tactic.Ring.of_eq
Mathlib.Tactic.Ring.add_congr
Mathlib.Tactic.Ring.sub_congr
Mathlib.Tactic.Ring.cast_pos
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
Mathlib.Tactic.Ring.atom_pf
Mathlib.Tactic.Ring.sub_pf
Mathlib.Tactic.Ring.neg_add
Mathlib.Tactic.Ring.neg_mul
Mathlib.Tactic.Ring.neg_one_mul
Mathlib.Meta.NormNum.IsInt.to_raw_eq
Mathlib.Meta.NormNum.isInt_mul
Mathlib.Meta.NormNum.IsInt.of_raw
Mathlib.Meta.NormNum.IsNat.to_isInt
Mathlib.Meta.NormNum.IsNat.of_raw
Mathlib.Tactic.Ring.neg_zero
Mathlib.Tactic.Ring.add_pf_add_lt
Mathlib.Tactic.Ring.add_pf_zero_add
Mathlib.Tactic.Ring.mul_congr
Mathlib.Tactic.Ring.add_mul
Mathlib.Tactic.Ring.mul_add
Mathlib.Tactic.Ring.mul_pf_left
Mathlib.Tactic.Ring.mul_pf_right
Mathlib.Tactic.Ring.one_mul
Mathlib.Tactic.Ring.mul_zero
Mathlib.Tactic.Ring.add_pf_add_zero
Mathlib.Tactic.Ring.zero_mul
Mathlib.Tactic.Ring.cast_zero
Nat.cast_zero
Mathlib.Tactic.Ring.add_pf_add_gt
Mathlib.Tactic.Ring.add_pf_add_overlap_zero
Mathlib.Meta.NormNum.IsInt.to_isNat
Mathlib.Meta.NormNum.isInt_add
Mathlib.Tactic.Ring.add_overlap_pf_zero
Mathlib.Meta.NormNum.IsNat.to_raw_eq
Mathlib.Tactic.Linarith.add_lt_of_neg_of_le
Mathlib.Tactic.Linarith.sub_neg_of_lt
Mathlib.Tactic.Linarith.sub_nonpos_of_le
mul_nonneg_of_nonpos_of_nonpos
AddGroup.existsAddOfLE
IsOrderedRing.toMulPosMono
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT
AddRightCancelSemigroup.toIsRightCancelAdd
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
div_le_one_of_leβ‚€
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
IsStrictOrderedRing.toMulPosStrictMono
IsStrictOrderedRing.toZeroLEOneClass
Mathlib.Tactic.Contrapose.contraposeβ‚„
Mathlib.Tactic.Linarith.eq_of_not_lt_of_not_gt
Mathlib.Tactic.Linarith.lt_of_eq_of_lt
sub_eq_zero_of_eq
AffineMap.lineMap_apply_one
AffineMap.lineMap_apply
eq_vadd_iff_vsub_eq
div_eq_mul_inv
mul_comm
SemigroupAction.mul_smul
eq_inv_smul_iffβ‚€
add_smul
sub_smul
one_smul
smul_sub
vsub_sub_vsub_cancel_right
vadd_vsub
smul_assoc
IsScalarTower.left
smul_add
vsub_add_vsub_cancel
trans_expand_right πŸ“–β€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”trans_right
IsStrictOrderedRing.toIsOrderedRing
trans_expand_left
trans_left πŸ“–β€”Wbtwβ€”β€”mul_nonneg
IsOrderedRing.toPosMulMono
mul_le_oneβ‚€
IsOrderedRing.toMulPosMono
AffineMap.lineMap_apply
AffineMap.lineMap_vsub_left
smul_smul
trans_left_ne πŸ“–β€”Wbtwβ€”β€”swap_right_iff
trans_left_right πŸ“–β€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”div_nonneg
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
sub_nonneg
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
mul_le_of_le_one_left
IsOrderedRing.toMulPosMono
mul_le_oneβ‚€
div_le_one_of_leβ‚€
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
IsStrictOrderedRing.toMulPosStrictMono
IsStrictOrderedRing.toZeroLEOneClass
sub_le_sub_right
vadd_vsub
smul_smul
vsub_vadd_eq_vsub_sub
smul_sub
div_mul_eq_mul_div
div_sub_div_same
mul_one
mul_sub
mul_div_assoc
sub_eq_zero
eq_of_le_of_not_lt
LT.lt.ne
mul_lt_one_of_nonneg_of_lt_one_right
sub_self
div_zero
MulZeroClass.mul_zero
zero_add
one_smul
div_self
Mathlib.Tactic.Ring.add_congr
Mathlib.Tactic.Ring.mul_congr
Mathlib.Tactic.Ring.sub_congr
Mathlib.Tactic.Ring.atom_pf
Mathlib.Tactic.Ring.add_mul
Mathlib.Tactic.Ring.mul_add
Mathlib.Tactic.Ring.mul_pf_right
Mathlib.Tactic.Ring.mul_pf_left
Mathlib.Tactic.Ring.one_mul
Mathlib.Tactic.Ring.mul_zero
Mathlib.Tactic.Ring.add_pf_add_zero
Mathlib.Tactic.Ring.zero_mul
Mathlib.Tactic.Ring.sub_pf
Mathlib.Tactic.Ring.neg_add
Mathlib.Tactic.Ring.neg_mul
Mathlib.Tactic.Ring.neg_one_mul
Mathlib.Meta.NormNum.IsInt.to_raw_eq
Mathlib.Meta.NormNum.isInt_mul
Mathlib.Meta.NormNum.IsInt.of_raw
Mathlib.Meta.NormNum.IsNat.to_isInt
Mathlib.Meta.NormNum.IsNat.of_raw
Mathlib.Tactic.Ring.neg_zero
Mathlib.Tactic.Ring.add_pf_add_lt
Mathlib.Tactic.Ring.add_pf_zero_add
Mathlib.Tactic.Ring.cast_pos
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
Mathlib.Tactic.Ring.mul_one
Mathlib.Tactic.Ring.add_pf_add_overlap_zero
Mathlib.Tactic.Ring.add_overlap_pf_zero
Mathlib.Meta.NormNum.IsInt.to_isNat
Mathlib.Meta.NormNum.isInt_add
Mathlib.Tactic.RingNF.nat_rawCast_1
pow_one
add_zero
trans_right πŸ“–β€”Wbtwβ€”β€”wbtw_comm
trans_left
trans_right_left πŸ“–β€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”wbtw_comm
IsStrictOrderedRing.toIsOrderedRing
trans_left_right
trans_right_ne πŸ“–β€”Wbtwβ€”β€”swap_left_iff
trans_sbtw_left πŸ“–β€”Wbtw
Sbtw
β€”β€”trans_left
Sbtw.wbtw
Sbtw.ne_left
Sbtw.right_ne
wbtw_swap_right_iff
trans_sbtw_right πŸ“–β€”Wbtw
Sbtw
β€”β€”sbtw_comm
trans_sbtw_left
wbtw_comm
vadd_const πŸ“–mathematicalWbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
β€”wbtw_vadd_const_iff
vsub_const πŸ“–mathematicalWbtwaddGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”wbtw_vsub_const_iff

(root)

Definitions

NameCategoryTheorems
Sbtw πŸ“–MathDef
44 mathmath: not_sbtw_self_right, not_sbtw_self, sbtw_iff_mem_image_Ioo_and_ne, Affine.Triangle.sbtw_touchpoint_singleton, EuclideanGeometry.Sphere.mem_commonExtTangents_iff, sbtw_midpoint_of_ne, sbtw_iff_left_ne_and_right_mem_image_Ioi, EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw, List.sbtw_cons, sbtw_vadd_const_iff, EuclideanGeometry.oangle_eq_pi_iff_sbtw, sbtw_const_vsub_iff, Affine.Triangle.touchpoint_singleton_sbtw, List.sbtw_four, sbtw_iff_right_ne_and_left_mem_image_Ioi, sbtw_const_sub_iff, EuclideanGeometry.Sphere.sbtw_secondInter, Affine.Simplex.mem_interior_face_iff_sbtw, Function.Injective.sbtw_map_iff, Sbtw.of_lt_of_lt, not_sbtw_self_left, sbtw_vsub_const_iff, sbtw_pointReflection_of_ne, sbtw_mul_sub_add_iff, EuclideanGeometry.Sphere.IsDiameter.sbtw, EuclideanGeometry.sbtw_of_collinear_of_dist_center_lt_radius, List.sbtw_iff_triplewise_and_ne_pair, sbtw_sub_const_iff, sbtw_add_const_iff, sbtw_comm, Affine.Triangle.sbtw_touchpoint_empty, sbtw_lineMap_iff, AffineSubspace.SOppSide.exists_sbtw, Set.InjOn.sbtw_map_iff, AffineEquiv.sbtw_map_iff, sbtw_zero_one_iff, sbtw_one_zero_iff, List.sbtw_triple, sbtw_const_add_iff, Collinear.sbtw_of_dist_eq_of_dist_lt, sbtw_neg_iff, EuclideanGeometry.angle_eq_pi_iff_sbtw, sbtw_const_vadd_iff, Affine.Simplex.mem_interior_iff_sbtw
Wbtw πŸ“–MathDef
64 mathmath: Collinear.wbtw_of_dist_eq_of_dist_le, EuclideanGeometry.Sphere.wbtw_secondInter, wbtw_sub_const_iff, EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw, wbtw_lineMap_iff, wbtw_const_vsub_iff, Sbtw.not_rotate, AffineSubspace.wOppSide_iff_exists_wbtw, EuclideanGeometry.Sphere.IsDiameter.wbtw, EuclideanGeometry.Sphere.IsExtTangentAt.wbtw, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, EuclideanGeometry.oangle_eq_zero_iff_wbtw, EuclideanGeometry.wbtw_of_collinear_of_dist_center_le_radius, IsClosed.exists_wbtw_isVisible, wbtw_swap_right_iff, List.wbtw_four, wbtw_zero_one_iff, List.wbtw_cons, wbtw_add_const_iff, Affine.Simplex.mem_closedInterior_face_iff_wbtw, wbtw_const_sub_iff, Wbtw.of_le_of_le, dist_add_dist_eq_iff, wbtw_comm, wbtw_iff_right_eq_or_left_mem_image_Ici, EuclideanGeometry.Sphere.IsIntTangentAt.wbtw, wbtw_iff_left_eq_or_right_mem_image_Ici, wbtw_const_add_iff, wbtw_one_zero_iff, Sbtw.not_swap_left, wbtw_self_iff, Affine.Simplex.mem_closedInterior_iff_wbtw, wbtw_self_left, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw, Set.InjOn.wbtw_map_iff, mem_segment_iff_wbtw, Sbtw.wbtw, List.wbtw_triple, Function.Injective.wbtw_map_iff, wbtw_vsub_const_iff, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, wbtw_swap_left_iff, wbtw_or_wbtw_smul_vadd_of_nonneg, dist_lt_dist_add_dist_iff, wbtw_const_vadd_iff, EuclideanGeometry.Sphere.mem_commonIntTangents_iff, wbtw_total_of_sameRay_vsub_left, Sbtw.not_swap_right, wbtw_or_wbtw_smul_vadd_of_nonpos, wbtw_vadd_const_iff, EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw, AffineIndependent.not_wbtw_of_injective, wbtw_neg_iff, wbtw_pointReflection, Collinear.wbtw_or_wbtw_or_wbtw, wbtw_midpoint, wbtw_iff_of_le, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, AffineEquiv.wbtw_map_iff, wbtw_mul_sub_add_iff, wbtw_iff_sameRay_vsub, wbtw_self_right, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, wbtw_rotate_iff
affineSegment πŸ“–CompOp
19 mathmath: mem_const_vadd_affineSegment, affineSegment_comm, mem_vadd_const_affineSegment, affineSegment.lift, affineSegment_same, Affine.Simplex.closedInterior_eq_affineSegment, affineSegment_const_vsub_image, affineSegment_const_vadd_image, affineSegment_eq_segment, affineSegment_vadd_const_image, mem_const_vsub_affineSegment, Affine.Simplex.closedInterior_face_eq_affineSegment, affineSegment_subset_affineSpan, affineSegment_vsub_const_image, mem_vsub_const_affineSegment, MeasureTheory.hausdorffMeasure_affineSegment, left_mem_affineSegment, affineSegment_image, right_mem_affineSegment

Theorems

NameKindAssumesProvesValidatesDepends On
affineSegment_comm πŸ“–mathematicalβ€”affineSegmentβ€”Set.ext
Set.sub_mem_Icc_iff_right
IsOrderedRing.toIsOrderedAddMonoid
sub_self
sub_zero
AffineMap.lineMap_apply_one_sub
affineSegment_const_vadd_image πŸ“–mathematicalβ€”Set.image
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
affineSegment
β€”affineSegment_image
affineSegment_const_vsub_image πŸ“–mathematicalβ€”Set.image
VSub.vsub
AddTorsor.toVSub
AddCommGroup.toAddGroup
affineSegment
addGroupIsAddTorsor
β€”affineSegment_image
affineSegment_eq_segment πŸ“–mathematicalβ€”affineSegment
addGroupIsAddTorsor
AddCommGroup.toAddGroup
segment
Ring.toSemiring
AddCommGroup.toAddCommMonoid
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”segment_eq_image_lineMap
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
affineSegment.eq_1
affineSegment_image πŸ“–mathematicalβ€”Set.image
DFunLike.coe
AffineMap
AffineMap.instFunLike
affineSegment
β€”affineSegment.eq_1
Set.image_image
AffineMap.comp_lineMap
affineSegment_same πŸ“–mathematicalβ€”affineSegment
Set
Set.instSingletonSet
β€”Set.image_congr
AffineMap.lineMap_same
Set.Nonempty.image_const
Set.nonempty_Icc
zero_le_one
IsOrderedRing.toZeroLEOneClass
affineSegment_subset_affineSpan πŸ“–mathematicalβ€”Set
Set.instHasSubset
affineSegment
SetLike.coe
AffineSubspace
AffineSubspace.instSetLike
affineSpan
Set.instInsert
Set.instSingletonSet
β€”affineSegment.eq_1
Set.subset_def
AffineMap.lineMap_mem_affineSpan_pair
affineSegment_vadd_const_image πŸ“–mathematicalβ€”Set.image
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
affineSegment
addGroupIsAddTorsor
β€”affineSegment_image
affineSegment_vsub_const_image πŸ“–mathematicalβ€”Set.image
VSub.vsub
AddTorsor.toVSub
AddCommGroup.toAddGroup
affineSegment
addGroupIsAddTorsor
β€”affineSegment_image
left_mem_affineSegment πŸ“–mathematicalβ€”Set
Set.instMembership
affineSegment
β€”Set.left_mem_Icc
zero_le_one
IsOrderedRing.toZeroLEOneClass
AffineMap.lineMap_apply_zero
mem_const_vadd_affineSegment πŸ“–mathematicalβ€”Set
Set.instMembership
affineSegment
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
β€”affineSegment_const_vadd_image
Function.Injective.mem_set_image
AddAction.injective
mem_const_vsub_affineSegment πŸ“–mathematicalβ€”Set
Set.instMembership
affineSegment
addGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”affineSegment_const_vsub_image
Function.Injective.mem_set_image
vsub_right_injective
mem_segment_iff_wbtw πŸ“–mathematicalβ€”Set
Set.instMembership
segment
Ring.toSemiring
AddCommGroup.toAddCommMonoid
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Wbtw
addGroupIsAddTorsor
β€”Wbtw.eq_1
affineSegment_eq_segment
mem_vadd_const_affineSegment πŸ“–mathematicalβ€”Set
Set.instMembership
affineSegment
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
addGroupIsAddTorsor
β€”affineSegment_vadd_const_image
Function.Injective.mem_set_image
vadd_right_injective
mem_vsub_const_affineSegment πŸ“–mathematicalβ€”Set
Set.instMembership
affineSegment
addGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”affineSegment_vsub_const_image
Function.Injective.mem_set_image
vsub_left_injective
not_sbtw_self πŸ“–mathematicalβ€”Sbtwβ€”Sbtw.left_ne_right
not_sbtw_self_left πŸ“–mathematicalβ€”Sbtwβ€”Sbtw.ne_left
not_sbtw_self_right πŸ“–mathematicalβ€”Sbtwβ€”Sbtw.ne_right
right_mem_affineSegment πŸ“–mathematicalβ€”Set
Set.instMembership
affineSegment
β€”Set.right_mem_Icc
zero_le_one
IsOrderedRing.toZeroLEOneClass
AffineMap.lineMap_apply_one
sbtw_add_const_iff πŸ“–mathematicalβ€”Sbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
β€”sbtw_vadd_const_iff
sbtw_comm πŸ“–mathematicalβ€”Sbtwβ€”Sbtw.eq_1
wbtw_comm
sbtw_const_add_iff πŸ“–mathematicalβ€”Sbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
β€”sbtw_const_vadd_iff
sbtw_const_sub_iff πŸ“–mathematicalβ€”Sbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
β€”sbtw_const_vsub_iff
sbtw_const_vadd_iff πŸ“–mathematicalβ€”Sbtw
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
β€”Sbtw.eq_1
wbtw_const_vadd_iff
AddAction.injective
sbtw_const_vsub_iff πŸ“–mathematicalβ€”Sbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”Sbtw.eq_1
wbtw_const_vsub_iff
vsub_right_injective
sbtw_iff_left_ne_and_right_mem_image_Ioi πŸ“–mathematicalβ€”Sbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ioi
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”Sbtw.left_ne
Wbtw.right_mem_image_Ici_of_left_ne
Sbtw.wbtw
LE.le.lt_or_eq
Set.mem_Ici
Set.mem_image_of_mem
AffineMap.lineMap_apply_one
wbtw_iff_left_eq_or_right_mem_image_Ici
Set.mem_of_mem_of_subset
Set.mem_Ioi
Set.Ioi_subset_Ici_self
AffineMap.lineMap_apply
vsub_ne_zero
vsub_vadd_eq_vsub_sub
one_smul
sub_smul
smul_ne_zero_iff
instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors
instIsDomain
GroupWithZero.toNoZeroSMulDivisors
IsDomain.toIsCancelMulZero
sub_ne_zero
LT.lt.ne
sbtw_iff_mem_image_Ioo_and_ne πŸ“–mathematicalβ€”Sbtw
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ioo
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”Sbtw.mem_image_Ioo
Sbtw.left_ne_right
Set.mem_Icc_of_Ioo
AffineMap.lineMap_apply
vsub_ne_zero
vadd_vsub_assoc
vsub_self
neg_vsub_eq_vsub_rev
neg_one_smul
add_smul
sub_eq_add_neg
add_zero
IsDomain.toIsCancelMulZero
LT.lt.ne
sbtw_iff_right_ne_and_left_mem_image_Ioi πŸ“–mathematicalβ€”Sbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ioi
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”sbtw_comm
IsStrictOrderedRing.toIsOrderedRing
sbtw_iff_left_ne_and_right_mem_image_Ioi
sbtw_lineMap_iff πŸ“–mathematicalβ€”Sbtw
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set
Set.instMembership
Set.Ioo
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”sbtw_iff_mem_image_Ioo_and_ne
Function.Injective.mem_set_image
AffineMap.lineMap_injective
sbtw_midpoint_of_ne πŸ“–mathematicalβ€”Sbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
midpoint
invertibleTwo
Semifield.toDivisionSemiring
Field.toSemifield
IsStrictOrderedRing.toCharZero
DivisionSemiring.toSemiring
β€”IsStrictOrderedRing.toCharZero
AffineEquiv.pointReflection_midpoint_left
sbtw_pointReflection_of_ne
sbtw_mul_sub_add_iff πŸ“–mathematicalβ€”Sbtw
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toMul
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
Set
Set.instMembership
Set.Ioo
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”sbtw_lineMap_iff
instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors
NoZeroDivisors.toNoZeroSMulDivisors
IsDomain.to_noZeroDivisors
sbtw_neg_iff πŸ“–mathematicalβ€”Sbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”β€”
sbtw_of_sbtw_of_sbtw_of_mem_affineSpan_pair πŸ“–β€”Sbtw
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Affine.Simplex.points
AffineSubspace
SetLike.instMembership
AffineSubspace.instSetLike
affineSpan
Set
Set.instInsert
Set.instSingletonSet
β€”β€”IsStrictOrderedRing.toIsOrderedRing
affineSpan_pair_le_of_mem_of_mem
mem_affineSpan
Set.mem_range_self
affineSpan_mono
AffineSubspace.le_def'
Wbtw.mem_affineSpan
Sbtw.wbtw
Sbtw.mem_image_Ioo
Set.mem_image
eq_affineCombination_of_mem_affineSpan_of_fintype
sign_eq_of_affineCombination_mem_affineSpan_single_lineMap
Affine.Simplex.independent
Finset.mem_univ
Finset.affineCombination_affineCombinationSingleWeights
Finset.affineCombination_affineCombinationLineMapWeights
Sbtw.affineCombination_of_mem_affineSpan_pair
IsStrictOrderedRing.isDomain
AddGroup.existsAddOfLE
Finset.sum_affineCombinationSingleWeights
Finset.sum_affineCombinationLineMapWeights
Finset.affineCombinationSingleWeights_apply_self
Finset.affineCombinationLineMapWeights_apply_of_ne
sbtw_one_zero_iff
sign_pos
IsStrictOrderedRing.toZeroLEOneClass
NeZero.charZero_one
IsStrictOrderedRing.toCharZero
sign_sum
IsOrderedRing.toIsOrderedAddMonoid
Finset.univ_nonempty
LT.lt.ne'
LE.le.trans_lt
not_lt
lt_add_of_pos_right
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
Left.add_pos
Finset.sum_singleton
Finset.sum_insert
sbtw_one_zero_iff πŸ“–mathematicalβ€”Sbtw
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Set
Set.instMembership
Set.Ioo
PartialOrder.toPreorder
β€”sbtw_comm
sbtw_zero_one_iff
sbtw_pointReflection_of_ne πŸ“–mathematicalβ€”Sbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
DFunLike.coe
AffineEquiv
EquivLike.toFunLike
AffineEquiv.equivLike
AffineEquiv.pointReflection
β€”wbtw_pointReflection
AffineEquiv.pointReflection_self
Function.Involutive.injective
AffineEquiv.pointReflection_involutive
sbtw_sub_const_iff πŸ“–mathematicalβ€”Sbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
β€”sbtw_vsub_const_iff
sbtw_vadd_const_iff πŸ“–mathematicalβ€”Sbtw
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
addGroupIsAddTorsor
β€”Sbtw.eq_1
wbtw_vadd_const_iff
vadd_right_injective
sbtw_vsub_const_iff πŸ“–mathematicalβ€”Sbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”Sbtw.eq_1
wbtw_vsub_const_iff
vsub_left_injective
sbtw_zero_one_iff πŸ“–mathematicalβ€”Sbtw
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Set
Set.instMembership
Set.Ioo
PartialOrder.toPreorder
β€”Sbtw.eq_1
wbtw_zero_one_iff
Set.mem_Icc
Set.mem_Ioo
LE.le.lt_of_ne
LT.lt.le
LT.lt.ne'
LT.lt.ne
wbtw_add_const_iff πŸ“–mathematicalβ€”Wbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
β€”wbtw_vadd_const_iff
wbtw_comm πŸ“–mathematicalβ€”Wbtwβ€”Wbtw.eq_1
affineSegment_comm
wbtw_const_add_iff πŸ“–mathematicalβ€”Wbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
β€”wbtw_const_vadd_iff
wbtw_const_sub_iff πŸ“–mathematicalβ€”Wbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
β€”wbtw_const_vsub_iff
wbtw_const_vadd_iff πŸ“–mathematicalβ€”Wbtw
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
β€”mem_const_vadd_affineSegment
wbtw_const_vsub_iff πŸ“–mathematicalβ€”Wbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”mem_const_vsub_affineSegment
wbtw_iff_left_eq_or_right_mem_image_Ici πŸ“–mathematicalβ€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ici
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”LE.le.lt_or_eq
Set.mem_image
one_le_invβ‚€
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
vadd_vsub
smul_smul
inv_mul_cancelβ‚€
LT.lt.ne'
one_smul
vsub_vadd
AffineMap.lineMap_apply_zero
Set.image_congr
AffineMap.lineMap_same
Set.Nonempty.image_const
wbtw_self_left
IsStrictOrderedRing.toIsOrderedRing
inv_nonneg
LE.le.trans
zero_le_one
IsStrictOrderedRing.toZeroLEOneClass
Set.mem_Ici
inv_le_one_of_one_leβ‚€
LT.lt.trans_le
one_pos
NeZero.charZero_one
IsStrictOrderedRing.toCharZero
wbtw_iff_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Wbtw
DivisionRing.toRing
Field.toDivisionRing
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
β€”LE.le.eq_or_lt
le_antisymm_iff
wbtw_self_iff
IsStrictOrderedRing.toIsOrderedRing
sub_pos
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsUnit.div_mul_cancel
LT.lt.ne'
sub_add_cancel
instIsDomain
LT.lt.ne
IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
mul_nonneg_iff_of_pos_right
IsStrictOrderedRing.toMulPosStrictMono
mul_le_iff_le_one_left
IsOrderedRing.toMulPosMono
MulPosStrictMono.toMulPosReflectLE
wbtw_iff_right_eq_or_left_mem_image_Ici πŸ“–mathematicalβ€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.image
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Ici
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”wbtw_comm
IsStrictOrderedRing.toIsOrderedRing
wbtw_iff_left_eq_or_right_mem_image_Ici
wbtw_iff_sameRay_vsub πŸ“–mathematicalβ€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SameRay
Semifield.toCommSemiring
Field.toSemifield
AddCommGroup.toAddCommMonoid
VSub.vsub
AddTorsor.toVSub
AddCommGroup.toAddGroup
β€”Wbtw.sameRay_vsub
vsub_eq_zero_iff_eq
IsStrictOrderedRing.toIsOrderedRing
div_nonneg
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
LT.lt.le
add_nonneg
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
div_le_one_of_leβ‚€
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
IsStrictOrderedRing.toMulPosStrictMono
IsStrictOrderedRing.toZeroLEOneClass
le_add_of_nonneg_left
covariant_swap_add_of_covariant_add
inv_smul_smulβ‚€
LT.lt.ne'
vsub_vadd
smul_smul
vadd_vsub_assoc
smul_add
Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq
IsCancelMulZero.toIsLeftCancelMulZero
instIsCancelMulZero
Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul
Mathlib.Tactic.FieldSimp.subst_add
Mathlib.Tactic.FieldSimp.NF.mul_eq_eval
Mathlib.Tactic.FieldSimp.NF.div_eq_eval
Mathlib.Tactic.FieldSimp.NF.atom_eq_eval
Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons
one_mul
Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst
Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div
div_one
Mathlib.Tactic.FieldSimp.NF.eval_cons
Mathlib.Tactic.FieldSimp.zpow'_one
Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃
Mathlib.Tactic.FieldSimp.NF.inv_eq_eval
Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃
mul_one
Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁
Mathlib.Tactic.FieldSimp.NF.mul_eq_evalβ‚‚
Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval
Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero
Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero
ne_of_gt
add_pos'
Mathlib.Tactic.FieldSimp.NF.one_eq_eval
one_ne_zero
NeZero.one
GroupWithZero.toNontrivial
Mathlib.Tactic.Ring.of_eq
Mathlib.Tactic.Ring.cast_pos
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
one_smul
wbtw_lineMap_iff πŸ“–mathematicalβ€”Wbtw
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”AffineMap.lineMap_same_apply
Wbtw.eq_1
affineSegment.eq_1
Function.Injective.mem_set_image
AffineMap.lineMap_injective
wbtw_midpoint πŸ“–mathematicalβ€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
midpoint
invertibleTwo
Semifield.toDivisionSemiring
Field.toSemifield
IsStrictOrderedRing.toCharZero
DivisionSemiring.toSemiring
β€”IsStrictOrderedRing.toCharZero
AffineEquiv.pointReflection_midpoint_left
wbtw_pointReflection
wbtw_mul_sub_add_iff πŸ“–mathematicalβ€”Wbtw
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toMul
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”wbtw_lineMap_iff
instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors
NoZeroDivisors.toNoZeroSMulDivisors
IsDomain.to_noZeroDivisors
wbtw_neg_iff πŸ“–mathematicalβ€”Wbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”β€”
wbtw_one_zero_iff πŸ“–mathematicalβ€”Wbtw
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
β€”wbtw_comm
wbtw_zero_one_iff
wbtw_or_wbtw_smul_vadd_of_nonneg πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
EuclideanDomain.toCommRing
Field.toEuclideanDomain
Wbtw
DivisionRing.toRing
Field.toDivisionRing
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
β€”le_total
wbtw_smul_vadd_smul_vadd_of_nonneg_of_le
wbtw_or_wbtw_smul_vadd_of_nonpos πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
EuclideanDomain.toCommRing
Field.toEuclideanDomain
Wbtw
DivisionRing.toRing
Field.toDivisionRing
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
β€”le_total
wbtw_smul_vadd_smul_vadd_of_nonpos_of_le
wbtw_pointReflection πŸ“–mathematicalβ€”Wbtw
DivisionRing.toRing
Field.toDivisionRing
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
DFunLike.coe
AffineEquiv
EquivLike.toFunLike
AffineEquiv.equivLike
AffineEquiv.pointReflection
β€”Nat.instAtLeastTwoHAddOfNat
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
IsStrictOrderedRing.toIsOrderedRing
Mathlib.Meta.NormNum.isRat_le_true
Mathlib.Meta.NormNum.IsNNRat.to_isRat
Mathlib.Meta.NormNum.isNNRat_inv_pos
IsStrictOrderedRing.toCharZero
Mathlib.Meta.NormNum.IsNat.to_isNNRat
Mathlib.Meta.NormNum.isNat_ofNat
Mathlib.Meta.NormNum.instAtLeastTwo
Nat.cast_one
AffineMap.lineMap_apply
AffineEquiv.pointReflection_apply
vadd_vsub_assoc
two_smul
inv_smul_smulβ‚€
vsub_vadd
wbtw_rotate_iff πŸ“–mathematicalβ€”Wbtwβ€”wbtw_comm
wbtw_swap_right_iff
wbtw_self_iff πŸ“–mathematicalβ€”Wbtwβ€”Set.image_congr
AffineMap.lineMap_same
Set.Nonempty.image_const
IsOrderedRing.toZeroLEOneClass
wbtw_self_left
wbtw_self_left πŸ“–mathematicalβ€”Wbtwβ€”left_mem_affineSegment
wbtw_self_right πŸ“–mathematicalβ€”Wbtwβ€”right_mem_affineSegment
wbtw_smul_vadd_smul_vadd_of_nonneg_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
EuclideanDomain.toCommRing
Field.toEuclideanDomain
Wbtw
DivisionRing.toRing
Field.toDivisionRing
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
β€”div_nonneg
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
LE.le.trans
div_le_one_of_leβ‚€
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
IsStrictOrderedRing.toMulPosStrictMono
IsStrictOrderedRing.toZeroLEOneClass
zero_div
AffineMap.lineMap_apply_zero
zero_smul
zero_vadd
vadd_vsub
smul_smul
IsUnit.div_mul_cancel
LT.lt.ne
LT.lt.trans_le
LE.le.lt_of_ne'
wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
EuclideanDomain.toCommRing
Field.toEuclideanDomain
Wbtw
DivisionRing.toRing
Field.toDivisionRing
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
β€”wbtw_comm
IsStrictOrderedRing.toIsOrderedRing
wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg
wbtw_smul_vadd_smul_vadd_of_nonpos_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
EuclideanDomain.toCommRing
Field.toEuclideanDomain
Wbtw
DivisionRing.toRing
Field.toDivisionRing
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
β€”neg_smul_neg
wbtw_smul_vadd_smul_vadd_of_nonneg_of_le
Left.nonneg_neg_iff
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
neg_le_neg_iff
covariant_swap_add_of_covariant_add
wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
EuclideanDomain.toCommRing
Field.toEuclideanDomain
Wbtw
DivisionRing.toRing
Field.toDivisionRing
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
β€”neg_smul
neg_add_cancel
zero_vadd
sub_smul
sub_add_cancel
wbtw_smul_vadd_smul_vadd_of_nonneg_of_le
Left.nonneg_neg_iff
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
neg_le_sub_iff_le_add
le_add_iff_nonneg_left
covariant_swap_add_of_covariant_add
IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT
AddRightCancelSemigroup.toIsRightCancelAdd
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
wbtw_sub_const_iff πŸ“–mathematicalβ€”Wbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
β€”wbtw_vsub_const_iff
wbtw_swap_left_iff πŸ“–mathematicalβ€”Wbtwβ€”smul_eq_zero
IsDomain.toIsCancelMulZero
add_smul
sub_smul
smul_smul
smul_sub
vsub_vadd_eq_vsub_sub
vadd_vsub
vsub_eq_zero_iff_eq
AddSemigroupAction.add_vadd
AffineMap.lineMap_apply
le_antisymm
add_eq_zero_iff_neg_eq
mul_sub
mul_one
Left.neg_nonpos_iff
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
mul_nonneg
IsOrderedRing.toPosMulMono
sub_nonneg
covariant_swap_add_of_covariant_add
AffineMap.lineMap_apply_zero
AffineMap.lineMap_same_apply
wbtw_self_left
wbtw_swap_right_iff πŸ“–mathematicalβ€”Wbtwβ€”wbtw_comm
wbtw_swap_left_iff
wbtw_total_of_sameRay_vsub_left πŸ“–mathematicalSameRay
Semifield.toCommSemiring
Field.toSemifield
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddCommGroup.toAddCommMonoid
VSub.vsub
AddTorsor.toVSub
AddCommGroup.toAddGroup
Wbtw
DivisionRing.toRing
Field.toDivisionRing
β€”IsStrictOrderedRing.toIsOrderedRing
div_nonneg
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
LT.lt.le
div_le_one_of_leβ‚€
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
IsStrictOrderedRing.toMulPosStrictMono
IsStrictOrderedRing.toZeroLEOneClass
inv_smul_smulβ‚€
LT.lt.ne'
vsub_vadd
smul_smul
vadd_vsub_assoc
vsub_self
add_zero
Mathlib.Tactic.Ring.div_congr
Mathlib.Tactic.Ring.atom_pf
Mathlib.Tactic.Ring.div_pf
Mathlib.Tactic.Ring.inv_single
Mathlib.Tactic.Ring.inv_mul
Mathlib.Meta.NormNum.IsNat.to_raw_eq
Mathlib.Meta.NormNum.IsNNRat.to_isNat
Mathlib.Meta.NormNum.isNNRat_inv_pos
IsStrictOrderedRing.toCharZero
Mathlib.Meta.NormNum.IsNat.to_isNNRat
Mathlib.Meta.NormNum.IsNat.of_raw
Mathlib.Tactic.Ring.mul_pf_right
Mathlib.Tactic.Ring.one_mul
Mathlib.Tactic.Ring.add_mul
Mathlib.Tactic.Ring.mul_add
Mathlib.Tactic.Ring.mul_pf_left
Mathlib.Tactic.Ring.mul_zero
Mathlib.Tactic.Ring.add_pf_add_zero
Mathlib.Tactic.Ring.zero_mul
Mathlib.Tactic.RingNF.nat_rawCast_1
pow_one
mul_one
Mathlib.Tactic.Ring.mul_congr
Mathlib.Tactic.Ring.inv_congr
LE.total
wbtw_vadd_const_iff πŸ“–mathematicalβ€”Wbtw
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
addGroupIsAddTorsor
β€”mem_vadd_const_affineSegment
wbtw_vsub_const_iff πŸ“–mathematicalβ€”Wbtw
addGroupIsAddTorsor
AddCommGroup.toAddGroup
VSub.vsub
AddTorsor.toVSub
β€”mem_vsub_const_affineSegment
wbtw_zero_one_iff πŸ“–mathematicalβ€”Wbtw
Ring.toAddCommGroup
Semiring.toModule
Ring.toSemiring
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
β€”Wbtw.eq_1
affineSegment.eq_1
Set.mem_image
AffineMap.lineMap_apply_ring
MulZeroClass.mul_zero
mul_one
zero_add

---

← Back to Index