Documentation Verification Report

Basic

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

Statistics

MetricCount
DefinitionsconvexAddSubmonoid
1
Theoremsconvex, convex_ge, convex_gt, convex_le, convex_lt, convex_ge, convex_gt, convex_le, convex_lt, add, add_smul, add_smul_mem, add_smul_sub_mem, affine_image, affine_preimage, affinity, exists_mem_add_smul_eq, inter, is_linear_image, is_linear_preimage, lineMap_mem, linear_image, linear_preimage, mapsTo_lineMap, mem_smul_of_zero_mem, midpoint_mem, neg, openSegment_subset, ordConnected, prod, segment_subset, semilinear_image, setOf_const_imp, set_combo_subset, smul, smul_mem_of_zero_mem, smul_preimage, starConvex, starConvex_iff, sub, translate, translate_preimage_left, translate_preimage_right, vadd, Convex_subadditive_le, convex_iUnion, convex_sUnion, convex_ge, convex_gt, convex_le, convex_lt, convex_ge, convex_gt, convex_le, convex_lt, convex, convex_of_chain, convex, semilinear_range, convex, starConvex, coe_convexAddSubmonoid, convex_Icc, convex_Ici, convex_Ico, convex_Iic, convex_Iio, convex_Ioc, convex_Ioi, convex_Ioo, convex_empty, convex_halfSpace_ge, convex_halfSpace_gt, convex_halfSpace_le, convex_halfSpace_lt, convex_hyperplane, convex_iInter, convex_iInterβ‚‚, convex_iff_add_mem, convex_iff_div, convex_iff_forall_pos, convex_iff_openSegment_subset, convex_iff_ordConnected, convex_iff_pairwise_pos, convex_iff_pointwise_add_subset, convex_iff_segment_subset, convex_list_sum, convex_multiset_sum, convex_of_nonneg_surjective_algebraMap, convex_openSegment, convex_pi, convex_sInter, convex_segment, convex_singleton, convex_sum, convex_uIcc, convex_univ, convex_vadd, convex_zero, mem_convexAddSubmonoid
100
Total101

AffineSubspace

Theorems

NameKindAssumesProvesValidatesDepends On
convex πŸ“–mathematicalβ€”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
SetLike.coe
AffineSubspace
addGroupIsAddTorsor
instSetLike
β€”Convex.combo_eq_smul_sub_add
smul_vsub_vadd_mem

Antitone

Theorems

NameKindAssumesProvesValidatesDepends On
convex_ge πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLE
β€”Set.sep_univ
AntitoneOn.convex_ge
antitoneOn
convex_univ
convex_gt πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLT
β€”Set.sep_univ
AntitoneOn.convex_gt
antitoneOn
convex_univ
convex_le πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLE
β€”Set.sep_univ
AntitoneOn.convex_le
antitoneOn
convex_univ
convex_lt πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLT
β€”Set.sep_univ
AntitoneOn.convex_lt
antitoneOn
convex_univ

AntitoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
convex_ge πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Set
Set.instMembership
Preorder.toLE
β€”MonotoneOn.convex_le
convex_gt πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Set
Set.instMembership
Preorder.toLT
β€”MonotoneOn.convex_lt
convex_le πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Set
Set.instMembership
Preorder.toLE
β€”MonotoneOn.convex_ge
convex_lt πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Set
Set.instMembership
Preorder.toLT
β€”MonotoneOn.convex_gt

Convex

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set
Set.add
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”Set.add_image_prod
is_linear_image
prod
IsLinearMap.isLinearMap_add
add_smul πŸ“–mathematicalConvex
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
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
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
Set
Set.smulSet
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
Set.add
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”HasSubset.Subset.antisymm
Set.instAntisymmSubset
Set.add_smul_subset
exists_mem_add_smul_eq
add_smul_mem 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
Set
Set.instMembership
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”β€”Mathlib.Tactic.Module.NF.eq_of_eval_eq_eval
Mathlib.Tactic.Module.NF.add_eq_eval
Mathlib.Tactic.Module.NF.atom_eq_eval
Mathlib.Tactic.Module.NF.smul_eq_eval
Mathlib.Tactic.Module.NF.eval_algebraMap
AddCommMonoid.nat_isScalarTower
Mathlib.Tactic.Module.NF.add_eq_eval₁
zero_add
Mathlib.Tactic.Module.NF.add_eq_evalβ‚‚
Mathlib.Tactic.Module.NF.eq_cons_cons
eq_natCast
RingHom.instRingHomClass
Nat.cast_one
sub_eq_add_neg
mul_one
Mathlib.Tactic.Abel.term_atomg
Mathlib.Tactic.Abel.subst_into_addg
Mathlib.Tactic.Abel.subst_into_negg
Mathlib.Tactic.Abel.term_neg
neg_zero
Mathlib.Tactic.Abel.term_add_constg
Mathlib.Tactic.Abel.term_add_termg
Mathlib.Meta.NormNum.IsNat.to_eq
Mathlib.Meta.NormNum.IsInt.to_isNat
Mathlib.Meta.NormNum.isInt_add
Mathlib.Meta.NormNum.isInt_neg
Mathlib.Meta.NormNum.IsNat.to_isInt
Mathlib.Meta.NormNum.isNat_ofNat
Mathlib.Tactic.Abel.zero_termg
sub_nonneg_of_le
sub_add_cancel
add_smul_sub_mem πŸ“–mathematicalConvex
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
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
SubNegMonoid.toSub
β€”add_comm
lineMap_mem
affine_image πŸ“–mathematicalConvex
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
Set.image
DFunLike.coe
AffineMap
addGroupIsAddTorsor
AffineMap.instFunLike
β€”StarConvex.affine_image
affine_preimage πŸ“–mathematicalConvex
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
Set.preimage
DFunLike.coe
AffineMap
addGroupIsAddTorsor
AffineMap.instFunLike
β€”StarConvex.affine_preimage
affinity πŸ“–mathematicalConvex
CommSemiring.toSemiring
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.image
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”Set.image_image
vadd
smul
exists_mem_add_smul_eq πŸ“–mathematicalConvex
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
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
Set
Set.instMembership
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”em
add_zero
zero_smul
LE.le.lt_of_ne'
add_nonneg
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
add_eq_zero_iff_of_nonneg
covariant_swap_add_of_covariant_add
convex_iff_div
Mathlib.Tactic.Module.NF.eq_of_eval_eq_eval
Mathlib.Tactic.Module.NF.smul_eq_eval
Mathlib.Tactic.Module.NF.add_eq_eval
Mathlib.Tactic.Module.NF.atom_eq_eval
Mathlib.Tactic.Module.NF.eval_algebraMap
AddCommMonoid.nat_isScalarTower
Mathlib.Tactic.Module.NF.add_eq_eval₁
zero_add
Mathlib.Tactic.Module.NF.eq_cons_cons
eq_natCast
RingHom.instRingHomClass
Nat.cast_one
Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq
IsCancelMulZero.toIsLeftCancelMulZero
instIsCancelMulZero
Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul
Mathlib.Tactic.FieldSimp.NF.mul_eq_eval
Mathlib.Tactic.FieldSimp.subst_add
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_eval
Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃
Mathlib.Tactic.FieldSimp.NF.one_eq_eval
mul_one
Mathlib.Tactic.FieldSimp.NF.mul_eq_evalβ‚‚
Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero
Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero
ne_of_gt
one_ne_zero
NeZero.one
GroupWithZero.toNontrivial
Mathlib.Tactic.Ring.of_eq
Mathlib.Tactic.Ring.atom_pf
inter πŸ“–mathematicalConvexSet
Set.instInter
β€”StarConvex.inter
is_linear_image πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
IsLinearMap
Set.imageβ€”linear_image
is_linear_preimage πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
IsLinearMap
Set.preimageβ€”linear_preimage
lineMap_mem πŸ“–mathematicalConvex
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
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
AffineMap.instFunLike
AffineMap.lineMap
β€”mapsTo_lineMap
linear_image πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.image
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
LinearMap.instFunLike
β€”LinearMap.map_add
LinearMap.map_smul
linear_preimage πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.preimage
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
LinearMap.instFunLike
β€”Set.mem_preimage
LinearMap.map_add
LinearMap.map_smul_of_tower
LinearMap.IsScalarTower.compatibleSMul
IsScalarTower.left
mapsTo_lineMap πŸ“–mathematicalConvex
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
Set
Set.instMembership
Set.MapsTo
DFunLike.coe
AffineMap
Ring.toAddCommGroup
Semiring.toModule
addGroupIsAddTorsor
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AffineMap.instFunLike
AffineMap.lineMap
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
β€”segment_eq_image_lineMap
segment_subset
mem_smul_of_zero_mem πŸ“–mathematicalConvex
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
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
Set
Set.instMembership
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Preorder.toLE
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
Set.smulSetβ€”Set.mem_smul_set_iff_inv_smul_memβ‚€
LT.lt.ne'
LT.lt.trans_le
zero_lt_one
IsStrictOrderedRing.toZeroLEOneClass
NeZero.charZero_one
IsStrictOrderedRing.toCharZero
smul_mem_of_zero_mem
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
inv_nonneg
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
LE.le.trans
zero_le_one
inv_le_one_of_one_leβ‚€
midpoint_mem πŸ“–mathematicalConvex
Ring.toSemiring
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
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
Set
Set.instMembership
midpoint
addGroupIsAddTorsor
β€”Nat.instAtLeastTwoHAddOfNat
segment_subset
midpoint_mem_segment
neg πŸ“–mathematicalConvex
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
Set
Set.neg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”is_linear_preimage
IsLinearMap.isLinearMap_neg
openSegment_subset πŸ“–mathematicalConvex
Set
Set.instMembership
Set.instHasSubset
openSegment
β€”HasSubset.Subset.trans
Set.instIsTransSubset
openSegment_subset_segment
segment_subset
ordConnected πŸ“–mathematicalConvex
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
Algebra.toSMul
Semifield.toCommSemiring
CommSemiring.toSemiring
Algebra.id
Set.OrdConnected
PartialOrder.toPreorder
β€”convex_iff_ordConnected
prod πŸ“–mathematicalConvexProd.instAddCommMonoid
Prod.instSMul
SProd.sprod
Set
Set.instSProd
β€”StarConvex.prod
segment_subset πŸ“–mathematicalConvex
Set
Set.instMembership
Set.instHasSubset
segment
β€”convex_iff_segment_subset
semilinear_image πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
Set.image
LinearMap
LinearMap.instFunLike
β€”RingHomSurjective.is_surjective
map_zero
MonoidWithZeroHomClass.toZeroHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
Function.Injective.of_eq_imp_le
Eq.le
map_add
AddMonoidHomClass.toAddHomClass
RingHomClass.toAddMonoidHomClass
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
SemilinearMapClass.toAddHomClass
LinearMap.semilinearMapClass
LinearMap.map_smulβ‚›β‚—
setOf_const_imp πŸ“–mathematicalConvexsetOfβ€”instIsEmptyFalse
set_combo_subset πŸ“–mathematicalConvex
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Set
Set.instHasSubset
Set.add
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
Set.smulSet
β€”convex_iff_pointwise_add_subset
smul πŸ“–mathematicalConvex
CommSemiring.toSemiring
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set
Set.smulSet
β€”linear_image
smulCommClass_self
smul_mem_of_zero_mem 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
Set
Set.instMembership
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”β€”zero_add
add_smul_mem
smul_preimage πŸ“–mathematicalConvex
CommSemiring.toSemiring
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.preimageβ€”linear_preimage
smulCommClass_self
starConvex πŸ“–mathematicalConvex
Set
Set.instMembership
StarConvexβ€”β€”
starConvex_iff πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Nonempty
StarConvex
Set
Set.instMembership
β€”StarConvex.mem
starConvex
sub πŸ“–mathematicalConvex
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
Set
Set.sub
SubNegMonoid.toSub
β€”sub_eq_add_neg
add
neg
translate πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.image
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”vadd
translate_preimage_left πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.preimage
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”add_comm
translate_preimage_right
translate_preimage_right πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.preimage
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”one_smul
add_smul
add_add_add_comm
smul_add
vadd πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
HVAdd.hVAdd
Set
instHVAdd
Set.vaddSet
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddAction.toAddSemigroupAction
AddMonoid.toAddAction
β€”Set.image_congr
add
convex_singleton

Directed

Theorems

NameKindAssumesProvesValidatesDepends On
convex_iUnion πŸ“–mathematicalDirected
Set
Set.instHasSubset
Convex
Set.iUnionβ€”Set.mem_iUnion

DirectedOn

Theorems

NameKindAssumesProvesValidatesDepends On
convex_sUnion πŸ“–mathematicalDirectedOn
Set
Set.instHasSubset
Convex
Set.sUnionβ€”Set.sUnion_eq_iUnion
Directed.convex_iUnion
directedOn_iff_directed

Monotone

Theorems

NameKindAssumesProvesValidatesDepends On
convex_ge πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLE
β€”Set.sep_univ
MonotoneOn.convex_ge
monotoneOn
convex_univ
convex_gt πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLE
β€”Set.sep_univ
MonotoneOn.convex_le
monotoneOn
convex_univ
convex_le πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLE
β€”Set.sep_univ
MonotoneOn.convex_le
monotoneOn
convex_univ
convex_lt πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLE
β€”Set.sep_univ
MonotoneOn.convex_le
monotoneOn
convex_univ

MonotoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
convex_ge πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Set
Set.instMembership
Preorder.toLE
β€”convex_le
OrderDual.isOrderedAddMonoid
OrderDual.instPosSMulMono
dual
convex_gt πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Set
Set.instMembership
Preorder.toLT
β€”convex_lt
OrderDual.isOrderedAddMonoid
OrderDual.instPosSMulMono
dual
convex_le πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Set
Set.instMembership
Preorder.toLE
β€”LE.le.trans
max_rec'
Convex.combo_le_max
convex_lt πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Set
Set.instMembership
Preorder.toLT
β€”LE.le.trans_lt
max_rec'
Convex.combo_le_max

Set.OrdConnected

Theorems

NameKindAssumesProvesValidatesDepends On
convex πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”convex_of_chain
isChain_of_trichotomous
instTrichotomousLe
convex_of_chain πŸ“–mathematicalIsChain
Preorder.toLE
PartialOrder.toPreorder
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”convex_iff_segment_subset
IsChain.total
instReflLe
HasSubset.Subset.trans
Set.instIsTransSubset
segment_subset_Icc
out
segment_symm

Set.Subsingleton

Theorems

NameKindAssumesProvesValidatesDepends On
convex πŸ“–mathematicalSet.SubsingletonConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”convex_iff_pairwise_pos
pairwise

Submodule

Theorems

NameKindAssumesProvesValidatesDepends On
convex πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
SetLike.coe
Submodule
setLike
β€”AddMemClass.add_mem
AddSubmonoidClass.toAddMemClass
addSubmonoidClass
smul_mem
starConvex πŸ“–mathematicalβ€”StarConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
SetLike.coe
Submodule
setLike
β€”convex
zero_mem

Submodule.Convex

Theorems

NameKindAssumesProvesValidatesDepends On
semilinear_range πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
SetLike.coe
Submodule
Submodule.setLike
LinearMap.range
β€”Submodule.convex

(root)

Definitions

NameCategoryTheorems
convexAddSubmonoid πŸ“–CompOp
2 mathmath: coe_convexAddSubmonoid, mem_convexAddSubmonoid

Theorems

NameKindAssumesProvesValidatesDepends On
Convex_subadditive_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
Convex
setOf
β€”convex_iff_segment_subset
le_trans
add_le_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
smul_le_smul_of_nonneg_left
IsOrderedModule.toPosSMulMono
IsOrderedRing.toIsOrderedModule
add_smul
one_smul
le_refl
coe_convexAddSubmonoid πŸ“–mathematicalβ€”SetLike.coe
AddSubmonoid
Set
Set.addZeroClass
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddSubmonoid.instSetLike
convexAddSubmonoid
setOf
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”β€”
convex_Icc πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Icc
PartialOrder.toPreorder
β€”Set.Ici_inter_Iic
Convex.inter
convex_Ici
convex_Iic
convex_Ici πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Ici
PartialOrder.toPreorder
β€”convex_Iic
OrderDual.isOrderedAddMonoid
OrderDual.instPosSMulMono
convex_Ico πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Ico
PartialOrder.toPreorder
β€”Set.Ici_inter_Iio
Convex.inter
convex_Ici
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
PosSMulStrictMono.toPosSMulMono
convex_Iio
convex_Iic πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Iic
PartialOrder.toPreorder
β€”add_le_add
IsOrderedAddMonoid.toAddLeftMono
covariant_swap_add_of_covariant_add
smul_le_smul_of_nonneg_left
Convex.combo_self
convex_Iio πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Iio
PartialOrder.toPreorder
β€”LE.le.eq_or_lt
zero_smul
zero_add
one_smul
add_lt_add_of_lt_of_le
IsOrderedAddMonoid.toAddLeftMono
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
IsRightCancelAdd.addRightStrictMono_of_addRightMono
IsCancelAdd.toIsRightCancelAdd
IsOrderedCancelAddMonoid.toIsCancelAdd
covariant_swap_add_of_covariant_add
smul_lt_smul_of_pos_left
Set.mem_Iio
smul_le_smul_of_nonneg_left
PosSMulStrictMono.toPosSMulMono
LT.lt.le
Convex.combo_self
convex_Ioc πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Ioc
PartialOrder.toPreorder
β€”Set.Ioi_inter_Iic
Convex.inter
convex_Ioi
convex_Iic
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
PosSMulStrictMono.toPosSMulMono
convex_Ioi πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Ioi
PartialOrder.toPreorder
β€”convex_Iio
OrderDual.isOrderedAddCancelMonoid
OrderDual.instPosSMulStrictMono
convex_Ioo πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Ioo
PartialOrder.toPreorder
β€”Set.Ioi_inter_Iio
Convex.inter
convex_Ioi
convex_Iio
convex_empty πŸ“–mathematicalβ€”Convex
Set
Set.instEmptyCollection
β€”β€”
convex_halfSpace_ge πŸ“–mathematicalIsLinearMapConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLE
PartialOrder.toPreorder
β€”Convex.is_linear_preimage
convex_Ici
convex_halfSpace_gt πŸ“–mathematicalIsLinearMapConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLT
PartialOrder.toPreorder
β€”Convex.is_linear_preimage
convex_Ioi
convex_halfSpace_le πŸ“–mathematicalIsLinearMapConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLE
PartialOrder.toPreorder
β€”Convex.is_linear_preimage
convex_Iic
convex_halfSpace_lt πŸ“–mathematicalIsLinearMapConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
Preorder.toLT
PartialOrder.toPreorder
β€”Convex.is_linear_preimage
convex_Iio
convex_hyperplane πŸ“–mathematicalIsLinearMapConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
setOf
β€”Convex.inter
convex_halfSpace_le
convex_halfSpace_ge
convex_iInter πŸ“–mathematicalConvexSet.iInterβ€”convex_sInter
Set.sInter_range
Set.forall_mem_range
convex_iInterβ‚‚ πŸ“–mathematicalConvexSet.iInterβ€”convex_iInter
convex_iff_add_mem πŸ“–mathematicalβ€”Convex
Set
Set.instMembership
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”β€”
convex_iff_div πŸ“–mathematicalβ€”Convex
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
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
Set
Set.instMembership
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
β€”starConvex_iff_div
convex_iff_forall_pos πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set
Set.instMembership
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
β€”starConvex_iff_forall_pos
convex_iff_openSegment_subset πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set
Set.instHasSubset
openSegment
β€”starConvex_iff_openSegment_subset
convex_iff_ordConnected πŸ“–mathematicalβ€”Convex
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
Algebra.toSMul
Semifield.toCommSemiring
CommSemiring.toSemiring
Algebra.id
Set.OrdConnected
PartialOrder.toPreorder
β€”segment_eq_uIcc
convex_iff_pairwise_pos πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.Pairwise
β€”convex_iff_forall_pos
eq_or_ne
Convex.combo_self
convex_iff_pointwise_add_subset πŸ“–mathematicalβ€”Convex
Set
Set.instHasSubset
Set.add
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
Set.smulSet
β€”Set.add_mem_add
convex_iff_segment_subset πŸ“–mathematicalβ€”Convex
Set
Set.instHasSubset
segment
β€”starConvex_iff_segment_subset
convex_list_sum πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set
Set.add
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
Set.zero
β€”AddSubmonoid.list_sum_mem
convex_multiset_sum πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Multiset.sum
Set
Set.addCommMonoid
β€”AddSubmonoid.multiset_sum_mem
convex_of_nonneg_surjective_algebraMap πŸ“–β€”Set
Set.instHasSubset
Set.Ici
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Set.image
DFunLike.coe
RingHom
CommSemiring.toSemiring
RingHom.instFunLike
algebraMap
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”β€”algebraMap_smul
FaithfulSMul.algebraMap_eq_one_iff
algebraMap.coe_add
convex_openSegment πŸ“–mathematicalβ€”Convex
CommSemiring.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
openSegment
β€”convex_iff_openSegment_subset
IsStrictOrderedRing.toZeroLEOneClass
add_pos'
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
mul_pos
IsStrictOrderedRing.toPosMulStrictMono
Mathlib.Tactic.LinearCombination.eq_of_eq
IsCancelAdd.toIsRightCancelAdd
IsOrderedCancelAddMonoid.toIsCancelAdd
IsStrictOrderedRing.toIsOrderedCancelAddMonoid
Mathlib.Tactic.LinearCombination.add_eq_eq
Mathlib.Tactic.LinearCombination.mul_const_eq
mul_one
mul_add
Distrib.leftDistribClass
Mathlib.Tactic.Abel.subst_into_add
Mathlib.Tactic.Abel.term_atom
Mathlib.Tactic.Abel.term_add_const
zero_add
Mathlib.Tactic.Abel.const_add_term
add_zero
Mathlib.Tactic.Module.NF.eq_of_eval_eq_eval
Mathlib.Tactic.Module.NF.add_eq_eval
Mathlib.Tactic.Module.NF.smul_eq_eval
Mathlib.Tactic.Module.NF.atom_eq_eval
Mathlib.Tactic.Module.NF.eval_algebraMap
AddCommMonoid.nat_isScalarTower
Mathlib.Tactic.Module.NF.add_eq_eval₁
Mathlib.Tactic.Module.NF.add_eq_evalβ‚‚
Mathlib.Tactic.Module.NF.eq_cons_cons
eq_natCast
RingHom.instRingHomClass
Nat.cast_one
Mathlib.Tactic.Ring.of_eq
Mathlib.Tactic.Ring.mul_congr
Mathlib.Tactic.Ring.add_congr
Mathlib.Tactic.Ring.atom_pf
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.add_pf_add_lt
Mathlib.Tactic.Ring.add_pf_zero_add
Mathlib.Tactic.Ring.cast_pos
Mathlib.Meta.NormNum.isNat_ofNat
convex_pi πŸ“–mathematicalConvexPi.addCommMonoid
Pi.instSMul
Set.pi
β€”starConvex_pi
convex_sInter πŸ“–mathematicalConvexSet.sInterβ€”starConvex_sInter
convex_segment πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
segment
β€”add_nonneg
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
mul_nonneg
IsOrderedRing.toPosMulMono
add_add_add_comm
mul_add
Distrib.leftDistribClass
mul_one
Mathlib.Tactic.Module.NF.eq_of_eval_eq_eval
Mathlib.Tactic.Module.NF.add_eq_eval
Mathlib.Tactic.Module.NF.smul_eq_eval
Mathlib.Tactic.Module.NF.atom_eq_eval
Mathlib.Tactic.Module.NF.eval_algebraMap
AddCommMonoid.nat_isScalarTower
Mathlib.Tactic.Module.NF.add_eq_eval₁
zero_add
Mathlib.Tactic.Module.NF.add_eq_evalβ‚‚
Mathlib.Tactic.Module.NF.eq_cons_cons
eq_natCast
RingHom.instRingHomClass
Nat.cast_one
convex_singleton πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set
Set.instSingletonSet
β€”Set.Subsingleton.convex
Set.subsingleton_singleton
convex_sum πŸ“–mathematicalConvex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Finset.sum
Set
Set.addCommMonoid
β€”AddSubmonoid.sum_mem
convex_uIcc πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set.uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”convex_Icc
convex_univ πŸ“–mathematicalβ€”Convex
Set.univ
β€”starConvex_univ
convex_vadd πŸ“–mathematicalβ€”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
HVAdd.hVAdd
Set
instHVAdd
Set.vaddSet
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
addGroupIsAddTorsor
β€”neg_vadd_vadd
Convex.vadd
convex_zero πŸ“–mathematicalβ€”Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
Set
Set.zero
β€”convex_singleton
mem_convexAddSubmonoid πŸ“–mathematicalβ€”Set
AddSubmonoid
Set.addZeroClass
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SetLike.instMembership
AddSubmonoid.instSetLike
convexAddSubmonoid
Convex
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”β€”

---

← Back to Index