Documentation Verification Report

Uniform

📁 Source: Mathlib/Analysis/Normed/Group/Uniform.lean

Statistics

MetricCount
DefinitionsinstMulNorm, instNorm, instNormedAddCommGroup, instNormedCommGroup
4
Theoremsantilipschitz_of_bound, continuous_of_bound, isometry_iff_norm, isometry_of_norm, lipschitz_of_bound, lipschitz_of_bound_nnnorm, uniformContinuous_of_bound, add_lipschitzWith, add_sub_lipschitzWith, inv, le_mul_nnnorm, le_mul_nnnorm', le_mul_norm, le_mul_norm', le_mul_norm_div, le_mul_norm_sub, mul_div_lipschitzWith, mul_lipschitzWith, neg, of_inv, of_neg, mul_norm_bddAbove, norm_bddAbove, nnnorm_map_of_map_one, nnnorm_map_of_map_zero, norm_map_of_map_one, norm_map_of_map_zero, add, div, inv, mul, neg, norm_div_le, norm_div_le_of_le, norm_sub_le, norm_sub_le_of_le, of_inv, of_neg, sub, add, div, inv, mul, neg, nnorm_le_mul, nnorm_le_mul', norm_div_le, norm_div_le_of_le, norm_le_mul, norm_le_mul', norm_sub_le, norm_sub_le_of_le, of_inv, of_neg, sub, add, div, inv, mul, neg, of_inv, of_neg, sub, add, div, inv, mul, neg, of_inv, of_neg, sub, antilipschitz_of_bound, continuous_of_bound, isometry_iff_norm, isometry_of_norm, lipschitz_of_bound, lipschitz_of_bound_nnnorm, uniformContinuous_of_bound, to_isIsometricVAdd_left, to_isIsometricVAdd_right, to_isIsometricSMul_left, to_isIsometricSMul_right, bound_of_antilipschitz, toIsTopologicalAddGroup, to_isUniformAddGroup, to_lipschitzAdd, toIsTopologicalGroup, to_isUniformGroup, to_lipschitzMul, mk_eq_one_iff, mk_eq_zero_iff, nnnorm_mk, nnnorm_mk', norm_mk, norm_mk', bound_of_antilipschitz, abs_dist_sub_le_dist_add_add, abs_dist_sub_le_dist_mul_mul, antilipschitzWith_iff_exists_mul_le_norm, antilipschitzWith_iff_exists_mul_le_norm', antilipschitzWith_inv_iff, antilipschitzWith_neg_iff, cauchySeq_prod_of_eventually_eq, cauchySeq_sum_of_eventually_eq, dist_add_add_le, dist_add_add_le_of_le, dist_add_self_left, dist_add_self_right, dist_div_div_le, dist_div_div_le_of_le, dist_div_eq_dist_mul_left, dist_div_eq_dist_mul_right, dist_mul_mul_le, dist_mul_mul_le_of_le, dist_mul_self_left, dist_mul_self_right, dist_self_add_left, dist_self_add_right, dist_self_div_left, dist_self_div_right, dist_self_mul_left, dist_self_mul_right, dist_self_sub_left, dist_self_sub_right, dist_sub_eq_dist_add_left, dist_sub_eq_dist_add_right, dist_sub_sub_le, dist_sub_sub_le_of_le, edist_add_add_le, edist_mul_mul_le, lipschitzOnWith_iff_norm_div_le, lipschitzOnWith_iff_norm_sub_le, lipschitzOnWith_inv_iff, lipschitzOnWith_neg_iff, lipschitzWith_iff_norm_div_le, lipschitzWith_iff_norm_sub_le, lipschitzWith_inv_iff, lipschitzWith_neg_iff, lipschitzWith_one_nnnorm, lipschitzWith_one_nnnorm', lipschitzWith_one_norm, lipschitzWith_one_norm', locallyLipschitzOn_inv_iff, locallyLipschitzOn_neg_iff, locallyLipschitz_inv_iff, locallyLipschitz_neg_iff, nndist_add_add_le, nndist_mul_mul_le, nnnorm_map, nnnorm_map', norm_map, norm_map', uniformContinuous_nnnorm, uniformContinuous_nnnorm', uniformContinuous_norm, uniformContinuous_norm'
156
Total160

AddMonoidHomClass

Theorems

NameKindAssumesProvesValidatesDepends On
antilipschitz_of_bound 📖mathematicalReal
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
Real.instMul
NNReal.toReal
DFunLike.coe
AntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
AntilipschitzWith.of_le_mul_dist
dist_eq_norm_sub
map_sub
continuous_of_bound 📖mathematicalReal
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
DFunLike.coe
Real.instMul
Continuous
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
LipschitzWith.continuous
lipschitz_of_bound
isometry_iff_norm 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
DFunLike.coe
Norm.norm
SeminormedAddGroup.toNorm
isometry_iff_dist_eq
dist_eq_norm_sub
map_sub
sub_zero
isometry_of_norm 📖mathematicalNorm.norm
SeminormedAddGroup.toNorm
DFunLike.coe
Isometry
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
isometry_iff_norm
lipschitz_of_bound 📖mathematicalReal
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
DFunLike.coe
Real.instMul
LipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
Real.toNNReal
LipschitzWith.of_dist_le'
dist_eq_norm_sub
map_sub
lipschitz_of_bound_nnnorm 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
DFunLike.coe
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
LipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
lipschitz_of_bound
Real.toNNReal_coe
uniformContinuous_of_bound 📖mathematicalReal
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
DFunLike.coe
Real.instMul
UniformContinuous
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
LipschitzWith.uniformContinuous
lipschitz_of_bound

AntilipschitzWith

Theorems

NameKindAssumesProvesValidatesDepends On
add_lipschitzWith 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
LipschitzWith
NNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderNNReal
NNReal.instInv
NNReal.instSub
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
of_le_mul_dist
edist_ne_top
NNReal.coe_inv
div_eq_inv_mul
le_div_iff₀
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
IsStrictOrderedRing.toMulPosStrictMono
Real.instIsStrictOrderedRing
NNReal.coe_pos
tsub_pos_iff_lt
NNReal.instCanonicallyOrderedAdd
NNReal.instOrderedSub
mul_comm
NNReal.coe_sub
LT.lt.le
sub_mul
sub_le_sub
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
mul_le_dist
LipschitzWith.dist_le_mul
le_trans
le_abs_self
abs_dist_sub_le_dist_add_add
add_sub_lipschitzWith 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
LipschitzWith
Pi.instSub
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
NNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderNNReal
NNReal.instInv
NNReal.instSubadd_sub_cancel
add_lipschitzWith
inv 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
antilipschitzWith_inv_iff
le_mul_nnnorm 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
SeminormedAddGroup.toAddGroup
NNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
le_mul_norm
le_mul_nnnorm' 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
SeminormedGroup.toGroup
NNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedGroup.toNNNorm
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
le_mul_norm'
le_mul_norm 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
SeminormedAddGroup.toAddGroup
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
Real.instMul
NNReal.toReal
dist_zero_right
le_mul_dist
le_mul_norm' 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
SeminormedGroup.toGroup
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
Real.instMul
NNReal.toReal
dist_one_right
le_mul_dist
le_mul_norm_div 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedCommGroup.toNorm
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Real.instMul
NNReal.toReal
le_mul_dist
le_mul_norm_sub 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedAddCommGroup.toNorm
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Real.instMul
NNReal.toReal
dist_eq_norm_sub
le_mul_dist
mul_div_lipschitzWith 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
LipschitzWith
Pi.instDiv
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
NNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderNNReal
NNReal.instInv
NNReal.instSubmul_div_cancel
mul_lipschitzWith
mul_lipschitzWith 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
LipschitzWith
NNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderNNReal
NNReal.instInv
NNReal.instSub
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
of_le_mul_dist
edist_ne_top
NNReal.coe_inv
div_eq_inv_mul
le_div_iff₀
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
IsStrictOrderedRing.toMulPosStrictMono
Real.instIsStrictOrderedRing
NNReal.coe_pos
tsub_pos_iff_lt
NNReal.instCanonicallyOrderedAdd
NNReal.instOrderedSub
mul_comm
NNReal.coe_sub
LT.lt.le
sub_mul
sub_le_sub
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
mul_le_dist
LipschitzWith.dist_le_mul
le_trans
le_abs_self
abs_dist_sub_le_dist_mul_mul
neg 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
antilipschitzWith_neg_iff
of_inv 📖AntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
antilipschitzWith_inv_iff
of_neg 📖AntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
antilipschitzWith_neg_iff

CauchySeq

Theorems

NameKindAssumesProvesValidatesDepends On
mul_norm_bddAbove 📖mathematicalCauchySeq
PseudoMetricSpace.toUniformSpace
SeminormedGroup.toPseudoMetricSpace
Nat.instPreorder
BddAbove
Real
Real.instLE
Set.range
Norm.norm
SeminormedGroup.toNorm
cauchySeq_bdd
add_comm
LE.le.trans
norm_le_norm_add_norm_div'
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
LT.lt.le
SeminormedGroup.dist_eq
bddAbove_def
norm_bddAbove 📖mathematicalCauchySeq
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
Nat.instPreorder
BddAbove
Real
Real.instLE
Set.range
Norm.norm
SeminormedAddGroup.toNorm
cauchySeq_bdd
add_comm
LE.le.trans
norm_le_norm_add_norm_sub'
add_le_add_iff_left
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
LT.lt.le
SeminormedAddGroup.dist_eq
bddAbove_def
Set.mem_range

Isometry

Theorems

NameKindAssumesProvesValidatesDepends On
nnnorm_map_of_map_one 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
SeminormedGroup.toGroup
NNNorm.nnnorm
SeminormedGroup.toNNNorm
norm_map_of_map_one
nnnorm_map_of_map_zero 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
SeminormedAddGroup.toAddGroup
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
norm_map_of_map_zero
norm_map_of_map_one 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
SeminormedGroup.toGroup
Norm.norm
SeminormedGroup.toNorm
dist_one_right
dist_eq
norm_map_of_map_zero 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
SeminormedAddGroup.toAddGroup
Norm.norm
SeminormedAddGroup.toNorm
dist_zero_right
dist_eq

LipschitzOnWith

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
edist_add_add_le
add_le_add
IsOrderedAddMonoid.toAddLeftMono
ENNReal.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
add_mul
Distrib.rightDistribClass
div 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
NNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
div_eq_mul_inv
mul
inv
inv 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
lipschitzOnWith_inv_iff
mul 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
NNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
edist_mul_mul_le
add_le_add
IsOrderedAddMonoid.toAddLeftMono
ENNReal.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
add_mul
Distrib.rightDistribClass
neg 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
lipschitzOnWith_neg_iff
norm_div_le 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
Set
Set.instMembership
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
Real.instMul
NNReal.toReal
lipschitzOnWith_iff_norm_div_le
norm_div_le_of_le 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
Set
Set.instMembership
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
Real.instMul
NNReal.toReal
LE.le.trans
norm_div_le
mul_le_mul_of_nonneg_left
IsOrderedRing.toPosMulMono
Real.instIsOrderedRing
NNReal.coe_nonneg
norm_sub_le 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
Set
Set.instMembership
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
Real.instMul
NNReal.toReal
lipschitzOnWith_iff_norm_sub_le
norm_sub_le_of_le 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
Set
Set.instMembership
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
Real.instMul
NNReal.toReal
LE.le.trans
norm_sub_le
mul_le_mul_of_nonneg_left
IsOrderedRing.toPosMulMono
Real.instIsOrderedRing
NNReal.coe_nonneg
of_inv 📖LipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
lipschitzOnWith_inv_iff
of_neg 📖LipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
lipschitzOnWith_neg_iff
sub 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
sub_eq_add_neg
add
neg

LipschitzWith

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
lipschitzOnWith_univ
LipschitzOnWith.add
lipschitzOnWith
div 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
NNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
div_eq_mul_inv
mul
inv
inv 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
lipschitzWith_inv_iff
mul 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
NNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
LipschitzOnWith.mul
lipschitzOnWith
neg 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
lipschitzWith_neg_iff
nnorm_le_mul 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
SeminormedAddGroup.toAddGroup
NNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
norm_le_mul
nnorm_le_mul' 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
SeminormedGroup.toGroup
NNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedGroup.toNNNorm
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
norm_le_mul'
norm_div_le 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
Real.instMul
NNReal.toReal
lipschitzWith_iff_norm_div_le
norm_div_le_of_le 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
Real.instMul
NNReal.toReal
LE.le.trans
norm_div_le
mul_le_mul_of_nonneg_left
IsOrderedRing.toPosMulMono
Real.instIsOrderedRing
NNReal.coe_nonneg
norm_le_mul 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
SeminormedAddGroup.toAddGroup
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
Real.instMul
NNReal.toReal
dist_zero_right
dist_le_mul
norm_le_mul' 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
SeminormedGroup.toGroup
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
Real.instMul
NNReal.toReal
dist_one_right
dist_le_mul
norm_sub_le 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
Real.instMul
NNReal.toReal
lipschitzWith_iff_norm_sub_le
norm_sub_le_of_le 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
Real.instMul
NNReal.toReal
LE.le.trans
norm_sub_le
mul_le_mul_of_nonneg_left
IsOrderedRing.toPosMulMono
Real.instIsOrderedRing
NNReal.coe_nonneg
of_inv 📖LipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
lipschitzWith_inv_iff
of_neg 📖LipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
lipschitzWith_neg_iff
sub 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
sub_eq_add_neg
add
neg

LocallyLipschitz

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalLocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
locallyLipschitzOn_univ
LocallyLipschitzOn.add
locallyLipschitzOn
div 📖mathematicalLocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
div_eq_mul_inv
mul
inv
inv 📖mathematicalLocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
locallyLipschitz_inv_iff
mul 📖mathematicalLocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
LocallyLipschitzOn.mul
locallyLipschitzOn
neg 📖mathematicalLocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
locallyLipschitz_neg_iff
of_inv 📖LocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
locallyLipschitz_inv_iff
of_neg 📖LocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
locallyLipschitz_neg_iff
sub 📖mathematicalLocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
sub_eq_add_neg
add
neg

LocallyLipschitzOn

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalLocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Filter.inter_mem
LipschitzOnWith.add
LipschitzOnWith.mono
Set.inter_subset_left
Set.inter_subset_right
div 📖mathematicalLocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
div_eq_mul_inv
mul
inv
inv 📖mathematicalLocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
locallyLipschitzOn_inv_iff
mul 📖mathematicalLocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Filter.inter_mem
LipschitzOnWith.mul
LipschitzOnWith.mono
Set.inter_subset_left
Set.inter_subset_right
neg 📖mathematicalLocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
locallyLipschitzOn_neg_iff
of_inv 📖LocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
locallyLipschitzOn_inv_iff
of_neg 📖LocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
locallyLipschitzOn_neg_iff
sub 📖mathematicalLocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
sub_eq_add_neg
add
neg

MonoidHomClass

Theorems

NameKindAssumesProvesValidatesDepends On
antilipschitz_of_bound 📖mathematicalReal
Real.instLE
Norm.norm
SeminormedGroup.toNorm
Real.instMul
NNReal.toReal
DFunLike.coe
AntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
AntilipschitzWith.of_le_mul_dist
dist_eq_norm_div
map_div
continuous_of_bound 📖mathematicalReal
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DFunLike.coe
Real.instMul
Continuous
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedGroup.toPseudoMetricSpace
LipschitzWith.continuous
lipschitz_of_bound
isometry_iff_norm 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
DFunLike.coe
Norm.norm
SeminormedGroup.toNorm
dist_eq_norm_div
div_one
isometry_of_norm 📖mathematicalNorm.norm
SeminormedGroup.toNorm
DFunLike.coe
Isometry
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
isometry_iff_norm
lipschitz_of_bound 📖mathematicalReal
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DFunLike.coe
Real.instMul
LipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
Real.toNNReal
LipschitzWith.of_dist_le'
dist_eq_norm_div
map_div
lipschitz_of_bound_nnnorm 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedGroup.toNNNorm
DFunLike.coe
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
LipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
lipschitz_of_bound
Real.toNNReal_coe
uniformContinuous_of_bound 📖mathematicalReal
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DFunLike.coe
Real.instMul
UniformContinuous
PseudoMetricSpace.toUniformSpace
SeminormedGroup.toPseudoMetricSpace
LipschitzWith.uniformContinuous
lipschitz_of_bound

NormedAddGroup

Theorems

NameKindAssumesProvesValidatesDepends On
to_isIsometricVAdd_left 📖mathematicalIsIsometricVAdd
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddMonoid.toAddAction
Isometry.of_dist_eq
dist_eq_norm_sub
add_sub_add_left_eq_sub
to_isIsometricVAdd_right 📖mathematicalIsIsometricVAdd
AddOpposite
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddOpposite.instAddMonoid
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
AddAction.toAddSemigroupAction
AddMonoid.toOppositeAddAction
Isometry.of_dist_eq
dist_eq_norm_sub
add_sub_add_right_eq_sub

NormedGroup

Theorems

NameKindAssumesProvesValidatesDepends On
to_isIsometricSMul_left 📖mathematicalIsIsometricSMul
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
SemigroupAction.toSMul
Monoid.toSemigroup
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
MulAction.toSemigroupAction
Monoid.toMulAction
Isometry.of_dist_eq
dist_eq_norm_div
mul_div_mul_left_eq_div
to_isIsometricSMul_right 📖mathematicalIsIsometricSMul
MulOpposite
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
SemigroupAction.toSMul
Monoid.toSemigroup
MulOpposite.instMonoid
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
MulAction.toSemigroupAction
Monoid.toOppositeMulAction
Isometry.of_dist_eq
dist_eq_norm_div
mul_div_mul_right_eq_div

OneHomClass

Theorems

NameKindAssumesProvesValidatesDepends On
bound_of_antilipschitz 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
DFunLike.coe
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
Real.instMul
NNReal.toReal
AntilipschitzWith.le_mul_nnnorm'
map_one

SeminormedAddCommGroup

Theorems

NameKindAssumesProvesValidatesDepends On
toIsTopologicalAddGroup 📖mathematicalIsTopologicalAddGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
toPseudoMetricSpace
SeminormedAddGroup.toAddGroup
toSeminormedAddGroup
IsUniformAddGroup.to_topologicalAddGroup
to_isUniformAddGroup
to_isUniformAddGroup 📖mathematicalIsUniformAddGroup
PseudoMetricSpace.toUniformSpace
toPseudoMetricSpace
SeminormedAddGroup.toAddGroup
toSeminormedAddGroup
LipschitzWith.uniformContinuous
LipschitzWith.sub
LipschitzWith.prod_fst
LipschitzWith.prod_snd
to_lipschitzAdd 📖mathematicalLipschitzAdd
toPseudoMetricSpace
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
toSeminormedAddGroup
LipschitzWith.add
LipschitzWith.prod_fst
LipschitzWith.prod_snd

SeminormedCommGroup

Theorems

NameKindAssumesProvesValidatesDepends On
toIsTopologicalGroup 📖mathematicalIsTopologicalGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
toPseudoMetricSpace
SeminormedGroup.toGroup
toSeminormedGroup
IsUniformGroup.to_topologicalGroup
to_isUniformGroup
to_isUniformGroup 📖mathematicalIsUniformGroup
PseudoMetricSpace.toUniformSpace
toPseudoMetricSpace
SeminormedGroup.toGroup
toSeminormedGroup
LipschitzWith.uniformContinuous
LipschitzWith.div
LipschitzWith.prod_fst
LipschitzWith.prod_snd
to_lipschitzMul 📖mathematicalLipschitzMul
toPseudoMetricSpace
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
toSeminormedGroup
LipschitzWith.mul
LipschitzWith.prod_fst
LipschitzWith.prod_snd

SeparationQuotient

Definitions

NameCategoryTheorems
instMulNorm 📖CompOp
1 mathmath: norm_mk'
instNorm 📖CompOp
3 mathmath: instNormOneClass, norm_liftNormedAddGroupHom_apply_le, norm_mk
instNormedAddCommGroup 📖CompOp
12 mathmath: liftNormedAddGroupHom_normNoninc, norm_liftNormedAddGroupHom_apply_le, liftNormedAddGroupHomEquiv_apply, norm_normedMk_eq_one, norm_normedMk_le, normedMk_eq_zero_iff, norm_liftNormedAddGroupHom_le, nnnorm_mk, normedMk_apply, liftNormedAddGroupHom_apply, liftNormedAddGroupHomEquiv_symm_apply_coe, liftNormedAddGroupHom_norm_le
instNormedCommGroup 📖CompOp
1 mathmath: nnnorm_mk'

Theorems

NameKindAssumesProvesValidatesDepends On
mk_eq_one_iff 📖mathematicalUniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedCommGroup.toPseudoMetricSpace
SeparationQuotient
instOne
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
Norm.norm
SeminormedCommGroup.toNorm
Real
Real.instZero
norm_mk'
norm_eq_zero'
mk_eq_zero_iff 📖mathematicalUniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
SeparationQuotient
instZero
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
Norm.norm
SeminormedAddCommGroup.toNorm
Real
Real.instZero
norm_eq_zero
nnnorm_mk 📖mathematicalNNNorm.nnnorm
SeparationQuotient
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddCommGroup.toSeminormedAddCommGroup
instNormedAddCommGroup
nnnorm_mk' 📖mathematicalNNNorm.nnnorm
SeparationQuotient
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedCommGroup.toPseudoMetricSpace
SeminormedGroup.toNNNorm
SeminormedCommGroup.toSeminormedGroup
NormedCommGroup.toSeminormedCommGroup
instNormedCommGroup
norm_mk 📖mathematicalNorm.norm
SeparationQuotient
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
instNorm
SeminormedAddCommGroup.toNorm
norm_mk' 📖mathematicalNorm.norm
SeparationQuotient
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedCommGroup.toPseudoMetricSpace
instMulNorm
SeminormedCommGroup.toNorm

ZeroHomClass

Theorems

NameKindAssumesProvesValidatesDepends On
bound_of_antilipschitz 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
DFunLike.coe
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
Real.instMul
NNReal.toReal
AntilipschitzWith.le_mul_nnnorm
map_zero

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
abs_dist_sub_le_dist_add_add 📖mathematicalReal
Real.instLE
abs
Real.lattice
Real.instAddGroup
Real.instSub
Dist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
dist_add_right
NormedAddGroup.to_isIsometricVAdd_right
dist_add_left
NormedAddGroup.to_isIsometricVAdd_left
dist_comm
abs_dist_sub_le
abs_dist_sub_le_dist_mul_mul 📖mathematicalReal
Real.instLE
abs
Real.lattice
Real.instAddGroup
Real.instSub
Dist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
dist_mul_right
NormedGroup.to_isIsometricSMul_right
dist_mul_left
NormedGroup.to_isIsometricSMul_left
dist_comm
abs_dist_sub_le
antilipschitzWith_iff_exists_mul_le_norm 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
DFunLike.coe
Real
Real.instLT
Real.instZero
Real.instLE
Real.instMul
Norm.norm
SeminormedAddGroup.toNorm
inv_pos_of_pos
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
Right.add_pos_of_nonneg_of_pos
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
NNReal.coe_nonneg
Mathlib.Meta.Positivity.pos_of_isNat
Real.instIsOrderedRing
Real.instNontrivial
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
le_imp_le_of_le_of_le
mul_le_mul_of_nonneg_left
IsOrderedRing.toPosMulMono
AntilipschitzWith.le_mul_norm
map_zero
AddMonoidHomClass.toZeroHomClass
le_of_lt
le_refl
mul_assoc
mul_le_of_le_one_left
IsOrderedRing.toMulPosMono
norm_nonneg
Mathlib.Tactic.FieldSimp.le_eq_cancel_le
PosMulStrictMono.toPosMulMono
Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul
Mathlib.Tactic.FieldSimp.NF.mul_eq_eval
Mathlib.Tactic.FieldSimp.NF.inv_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.one_eq_eval
Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁
Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval
Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg
LT.lt.ne'
Mathlib.Tactic.FieldSimp.NF.cons_pos
Real.instZeroLEOneClass
zero_lt_one
NeZero.one
GroupWithZero.toNontrivial
le_add_iff_nonneg_right
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
zero_le_one
AddMonoidHomClass.antilipschitz_of_bound
inv_mul_cancel_left₀
antilipschitzWith_iff_exists_mul_le_norm' 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
DFunLike.coe
Real
Real.instLT
Real.instZero
Real.instLE
Real.instMul
Norm.norm
SeminormedGroup.toNorm
inv_pos_of_pos
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
Right.add_pos_of_nonneg_of_pos
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
NNReal.coe_nonneg
Mathlib.Meta.Positivity.pos_of_isNat
Real.instIsOrderedRing
Real.instNontrivial
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
le_imp_le_of_le_of_le
mul_le_mul_of_nonneg_left
IsOrderedRing.toPosMulMono
AntilipschitzWith.le_mul_norm'
map_one
MonoidHomClass.toOneHomClass
le_of_lt
le_refl
mul_assoc
mul_le_of_le_one_left
IsOrderedRing.toMulPosMono
norm_nonneg'
Mathlib.Tactic.FieldSimp.le_eq_cancel_le
PosMulStrictMono.toPosMulMono
Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul
Mathlib.Tactic.FieldSimp.NF.mul_eq_eval
Mathlib.Tactic.FieldSimp.NF.inv_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.one_eq_eval
Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁
Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval
Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg
LT.lt.ne'
Mathlib.Tactic.FieldSimp.NF.cons_pos
Real.instZeroLEOneClass
zero_lt_one
NeZero.one
GroupWithZero.toNontrivial
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
MonoidHomClass.antilipschitz_of_bound
inv_mul_cancel_left₀
antilipschitzWith_inv_iff 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
edist_inv_inv
NormedGroup.to_isIsometricSMul_left
NormedGroup.to_isIsometricSMul_right
antilipschitzWith_neg_iff 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
edist_neg_neg
NormedAddGroup.to_isIsometricVAdd_left
NormedAddGroup.to_isIsometricVAdd_right
cauchySeq_prod_of_eventually_eq 📖CauchySeq
PseudoMetricSpace.toUniformSpace
SeminormedCommGroup.toPseudoMetricSpace
Nat.instPreorder
Finset.prod
CommGroup.toCommMonoid
SeminormedCommGroup.toCommGroup
Finset.range
Finset.prod_div_distrib
div_mul_cancel
Finset.eventually_constant_prod
le_of_lt
div_self'
add_le_add_left
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
CauchySeq.mul
SeminormedCommGroup.to_isUniformGroup
Filter.Tendsto.cauchySeq
tendsto_atTop_of_eventually_const
cauchySeq_sum_of_eventually_eq 📖CauchySeq
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Nat.instPreorder
Finset.sum
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
Finset.range
Finset.sum_sub_distrib
sub_add_cancel
Finset.eventually_constant_sum
le_of_lt
sub_self
add_le_add_left
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
CauchySeq.add
SeminormedAddCommGroup.to_isUniformAddGroup
Filter.Tendsto.cauchySeq
tendsto_atTop_of_eventually_const
dist_add_add_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Real.instAdd
dist_add_right
NormedAddGroup.to_isIsometricVAdd_right
dist_add_left
NormedAddGroup.to_isIsometricVAdd_left
dist_triangle
dist_add_add_le_of_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Real.instAdd
LE.le.trans
dist_add_add_le
add_le_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
dist_add_self_left 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedAddGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
Norm.norm
SeminormedAddGroup.toNorm
dist_comm
dist_add_self_right
dist_add_self_right 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedAddGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
Norm.norm
SeminormedAddGroup.toNorm
dist_zero_left
dist_add_right
NormedAddGroup.to_isIsometricVAdd_right
zero_add
dist_div_div_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Real.instAdd
div_eq_mul_inv
dist_inv_inv
NormedGroup.to_isIsometricSMul_left
NormedGroup.to_isIsometricSMul_right
dist_mul_mul_le
dist_div_div_le_of_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Real.instAdd
LE.le.trans
dist_div_div_le
add_le_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
dist_div_eq_dist_mul_left 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedGroup.toPseudoMetricSpace
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
dist_mul_right
NormedGroup.to_isIsometricSMul_right
div_mul_cancel
dist_div_eq_dist_mul_right 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedGroup.toPseudoMetricSpace
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
dist_mul_right
NormedGroup.to_isIsometricSMul_right
div_mul_cancel
dist_mul_mul_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Real.instAdd
dist_mul_right
NormedGroup.to_isIsometricSMul_right
dist_mul_left
NormedGroup.to_isIsometricSMul_left
dist_triangle
dist_mul_mul_le_of_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Real.instAdd
LE.le.trans
dist_mul_mul_le
add_le_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
dist_mul_self_left 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
Norm.norm
SeminormedGroup.toNorm
dist_comm
dist_mul_self_right
dist_mul_self_right 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
Norm.norm
SeminormedGroup.toNorm
dist_one_left
dist_mul_right
NormedGroup.to_isIsometricSMul_right
one_mul
dist_self_add_left 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Norm.norm
SeminormedAddCommGroup.toNorm
dist_comm
dist_self_add_right
dist_self_add_right 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Norm.norm
SeminormedAddCommGroup.toNorm
dist_zero_left
dist_add_left
NormedAddGroup.to_isIsometricVAdd_left
add_zero
dist_self_div_left 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Norm.norm
SeminormedCommGroup.toNorm
dist_comm
dist_self_div_right
dist_self_div_right 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Norm.norm
SeminormedCommGroup.toNorm
div_eq_mul_inv
dist_self_mul_right
norm_inv'
dist_self_mul_left 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Norm.norm
SeminormedCommGroup.toNorm
dist_comm
dist_self_mul_right
dist_self_mul_right 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Norm.norm
SeminormedCommGroup.toNorm
dist_one_left
dist_mul_left
NormedGroup.to_isIsometricSMul_left
mul_one
dist_self_sub_left 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Norm.norm
SeminormedAddCommGroup.toNorm
dist_comm
dist_self_sub_right
dist_self_sub_right 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Norm.norm
SeminormedAddCommGroup.toNorm
sub_eq_add_neg
dist_self_add_right
norm_neg
dist_sub_eq_dist_add_left 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedAddGroup.toPseudoMetricSpace
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
dist_add_right
NormedAddGroup.to_isIsometricVAdd_right
sub_add_cancel
dist_sub_eq_dist_add_right 📖mathematicalDist.dist
PseudoMetricSpace.toDist
SeminormedAddGroup.toPseudoMetricSpace
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
dist_add_right
NormedAddGroup.to_isIsometricVAdd_right
sub_add_cancel
dist_sub_sub_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Real.instAdd
sub_eq_add_neg
dist_neg_neg
NormedAddGroup.to_isIsometricVAdd_left
NormedAddGroup.to_isIsometricVAdd_right
dist_add_add_le
dist_sub_sub_le_of_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
SeminormedAddCommGroup.toPseudoMetricSpace
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Real.instAdd
LE.le.trans
dist_sub_sub_le
add_le_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
edist_add_add_le 📖mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
ENNReal.instPartialOrder
EDist.edist
PseudoEMetricSpace.toEDist
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
edist_nndist
ENNReal.coe_le_coe
nndist_add_add_le
edist_mul_mul_le 📖mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
ENNReal.instPartialOrder
EDist.edist
PseudoEMetricSpace.toEDist
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
edist_nndist
nndist_mul_mul_le
lipschitzOnWith_iff_norm_div_le 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
Real.instMul
NNReal.toReal
dist_eq_norm_div
lipschitzOnWith_iff_norm_sub_le 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
Real.instMul
NNReal.toReal
lipschitzOnWith_iff_dist_le_mul
dist_eq_norm_sub
lipschitzOnWith_inv_iff 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
edist_inv_inv
NormedGroup.to_isIsometricSMul_left
NormedGroup.to_isIsometricSMul_right
lipschitzOnWith_neg_iff 📖mathematicalLipschitzOnWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
edist_neg_neg
NormedAddGroup.to_isIsometricVAdd_left
NormedAddGroup.to_isIsometricVAdd_right
lipschitzWith_iff_norm_div_le 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedGroup.toNorm
DivInvMonoid.toDiv
Group.toDivInvMonoid
SeminormedGroup.toGroup
Real.instMul
NNReal.toReal
dist_eq_norm_div
lipschitzWith_iff_norm_sub_le 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
Real
Real.instLE
Norm.norm
SeminormedAddGroup.toNorm
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
Real.instMul
NNReal.toReal
lipschitzWith_iff_dist_le_mul
dist_eq_norm_sub
lipschitzWith_inv_iff 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
edist_inv_inv
NormedGroup.to_isIsometricSMul_left
NormedGroup.to_isIsometricSMul_right
lipschitzWith_neg_iff 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
edist_neg_neg
NormedAddGroup.to_isIsometricVAdd_left
NormedAddGroup.to_isIsometricVAdd_right
lipschitzWith_one_nnnorm 📖mathematicalLipschitzWith
NNReal
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
EMetricSpace.toPseudoEMetricSpace
MetricSpace.toEMetricSpace
instMetricSpaceNNReal
instOneNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
lipschitzWith_one_norm
lipschitzWith_one_nnnorm' 📖mathematicalLipschitzWith
NNReal
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
EMetricSpace.toPseudoEMetricSpace
MetricSpace.toEMetricSpace
instMetricSpaceNNReal
instOneNNReal
NNNorm.nnnorm
SeminormedGroup.toNNNorm
lipschitzWith_one_norm'
lipschitzWith_one_norm 📖mathematicalLipschitzWith
Real
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddGroup.toPseudoMetricSpace
EMetricSpace.toPseudoEMetricSpace
MetricSpace.toEMetricSpace
Real.metricSpace
NNReal
instOneNNReal
Norm.norm
SeminormedAddGroup.toNorm
dist_zero
LipschitzWith.dist_right
lipschitzWith_one_norm' 📖mathematicalLipschitzWith
Real
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedGroup.toPseudoMetricSpace
EMetricSpace.toPseudoEMetricSpace
MetricSpace.toEMetricSpace
Real.metricSpace
NNReal
instOneNNReal
Norm.norm
SeminormedGroup.toNorm
dist_one
LipschitzWith.dist_right
locallyLipschitzOn_inv_iff 📖mathematicalLocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
locallyLipschitzOn_neg_iff 📖mathematicalLocallyLipschitzOn
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
lipschitzOnWith_neg_iff
locallyLipschitz_inv_iff 📖mathematicalLocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedCommGroup.toPseudoMetricSpace
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
SeminormedCommGroup.toCommGroup
locallyLipschitz_neg_iff 📖mathematicalLocallyLipschitz
PseudoMetricSpace.toPseudoEMetricSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Pi.instNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
lipschitzOnWith_neg_iff
nndist_add_add_le 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNDist.nndist
PseudoMetricSpace.toNNDist
SeminormedAddCommGroup.toPseudoMetricSpace
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
NNReal.coe_le_coe
dist_add_add_le
nndist_mul_mul_le 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNDist.nndist
PseudoMetricSpace.toNNDist
SeminormedCommGroup.toPseudoMetricSpace
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
SeminormedGroup.toGroup
SeminormedCommGroup.toSeminormedGroup
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
NNReal.coe_le_coe
dist_mul_mul_le
nnnorm_map 📖mathematicalNNNorm.nnnorm
SeminormedAddGroup.toNNNorm
DFunLike.coe
NNReal.eq
norm_map
nnnorm_map' 📖mathematicalNNNorm.nnnorm
SeminormedGroup.toNNNorm
DFunLike.coe
NNReal.eq
norm_map'
norm_map 📖mathematicalNorm.norm
SeminormedAddGroup.toNorm
DFunLike.coe
Isometry.norm_map_of_map_zero
IsometryClass.isometry
map_zero
norm_map' 📖mathematicalNorm.norm
SeminormedGroup.toNorm
DFunLike.coe
Isometry.norm_map_of_map_one
IsometryClass.isometry
map_one
uniformContinuous_nnnorm 📖mathematicalUniformContinuous
NNReal
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
instPseudoMetricSpaceNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
uniformContinuous_norm
norm_nonneg
uniformContinuous_nnnorm' 📖mathematicalUniformContinuous
NNReal
PseudoMetricSpace.toUniformSpace
SeminormedGroup.toPseudoMetricSpace
instPseudoMetricSpaceNNReal
NNNorm.nnnorm
SeminormedGroup.toNNNorm
uniformContinuous_norm'
norm_nonneg'
uniformContinuous_norm 📖mathematicalUniformContinuous
Real
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
Real.pseudoMetricSpace
Norm.norm
SeminormedAddGroup.toNorm
LipschitzWith.uniformContinuous
lipschitzWith_one_norm
uniformContinuous_norm' 📖mathematicalUniformContinuous
Real
PseudoMetricSpace.toUniformSpace
SeminormedGroup.toPseudoMetricSpace
Real.pseudoMetricSpace
Norm.norm
SeminormedGroup.toNorm
LipschitzWith.uniformContinuous
lipschitzWith_one_norm'

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