Documentation Verification Report

Basic

πŸ“ Source: Mathlib/RingTheory/Valuation/ValuativeRel/Basic.lean

Statistics

MetricCount
DefinitionsIsValuativeTopology, Compatible, ValuativeExtension, mapPosSubmonoid, mapValueGroupWithZero, ValuativePreorder, IsDiscrete, IsNontrivial, IsRankLeOne, RankLeOneStruct, emb, SRel, ValueGroupWithZero, embed, liftβ‚‚, mk, WithPreorder, instBotValueGroupWithZero, instCommMonoidWithZeroValueGroupWithZero, instCommRingWithPreorder, instInvValueGroupWithZero, instLEValueGroupWithZero, instLinearOrderValueGroupWithZero, instLinearOrderedCommGroupWithZeroValueGroupWithZero, instMulValueGroupWithZero, instOneValueGroupWithZero, instOrderBotValueGroupWithZero, instPreorderWithPreorder, instTransVeq, instTransVle, instWithPreorder, instZeroValueGroupWithZero, ofValuation, posSubmonoid, supp, uniformizer, valuation, valueSetoid, veq, vle, vlt, Β«term_<α΅₯_Β», Β«term_=α΅₯_Β», Β«term_≀α΅₯_Β»
44
Theoremsmem_nhds_iff, ofValuation, srel_iff_lt, vle_iff_le, apply_posSubmonoid_ne_zero, apply_posSubmonoid_pos, one_rel_iff, one_srel_iff, one_vle_iff, one_vlt_iff, rel_iff_le, rel_one_iff, srel_iff_lt, srel_one_iff, veq_iff_eq, vle_iff_le, vle_one_iff, vlt_iff_lt, vlt_one_iff, compatible_comap, mapPosSubmonoid_apply_coe, mapValueGroupWithZero_mk, mapValueGroupWithZero_strictMono, mapValueGroupWithZero_valuation, srel_iff_srel, vle_iff_vle, vlt_iff_vlt, vle_iff_le, has_maximal_element, condition, exists_lt_one, nonempty, of_valuativeExtension, strictMono, refl, rfl, trans, trans', trans_srel, rel, trans, trans_rel, bot_eq_zero, embed_mk, embed_strictMono, embed_valuation, exact, ind, inv_mk, lift_mk, lift_mul, lift_one, lift_valuation, lift_zero, liftβ‚‚_mk, mk_eq_div, mk_eq_mk, mk_eq_one, mk_eq_valuation, mk_eq_zero, mk_le_mk, mk_lt_mk, mk_mul_mk, mk_one_one, mk_pos, mk_self, mk_zero, sound, div_rel_iff, div_rel_one_iff, div_vle_iff, div_vle_one_iff, exists_valuation_div_valuation_eq, exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, ext, ext_iff, instCompatibleValueGroupWithZeroValuation, instIsNontrivialOfIsNontrivialOfCompatible, instIsOrderedMonoidValueGroupWithZero, instIsPrimeSupp, instMulArchimedeanValueGroupWithZeroOfIsRankLeOne, instReflVeq, instReflVle, instSymmVeq, instValuativePreorderWithPreorder, inv_rel_one, inv_srel_one, inv_vle_one, inv_vlt_one, isEquiv, isNontrivial_iff_isNontrivial, isNontrivial_iff_nontrivial_units, le_uniformizer_iff, left_cancel_posSubmonoid, mul_rel_mul, mul_rel_mul_iff_left, mul_rel_mul_iff_right, mul_srel_mul, mul_srel_mul_iff_left, mul_srel_mul_iff_right, mul_srel_mul_of_rel_of_srel, mul_srel_mul_of_srel_of_rel, mul_veq_mul, mul_vle_mul, mul_vle_mul_iff_left, mul_vle_mul_iff_right, mul_vle_mul_left, mul_vle_mul_right, mul_vlt_mul, mul_vlt_mul_iff_left, mul_vlt_mul_iff_right, mul_vlt_mul_left, mul_vlt_mul_of_vle_of_vlt, mul_vlt_mul_of_vlt_of_vle, mul_vlt_mul_right, not_rel_one_zero, not_srel_iff, not_vgt_of_veq, not_vle, not_vle_one_zero, not_vlt, not_vlt_of_veq, not_vlt_zero, one_apply_posSubmonoid, one_rel_div_iff, one_rel_inv, one_srel_inv, one_vle_div_iff, one_vle_inv, one_vlt_inv, posSubmonoid_def, pow_rel_pow, pow_rel_pow_of_one_rel, pow_rel_pow_of_rel_one, pow_srel_pow, pow_vle_pow, pow_vle_pow_of_one_vle, pow_vle_pow_of_vle_one, pow_vlt_pow, rel_add, rel_add_cases, rel_div_iff, rel_mul, rel_mul_cancel, rel_mul_left, rel_mul_left_iff, rel_mul_right, rel_mul_right_iff, rel_refl, rel_rfl, rel_total, rel_trans, rel_trans', rel_zero_iff, right_cancel_posSubmonoid, srel_iff, srel_mul_left, srel_mul_left_iff, srel_mul_right, srel_mul_right_iff, srel_of_rel_of_srel, srel_of_srel_of_rel, supp_def, supp_eq_valuation_supp, uniformizer_inv_le_iff, uniformizer_lt_one, uniformizer_ne_zero, uniformizer_pos, val_posSubmonoid_ne_zero, valuation_eq_zero_iff, valuation_posSubmonoid_ne_zero, valuation_surjective, not_vgt, not_vlt, refl, rfl, vge, vle, veq_comm, veq_def, veq_refl, veq_rfl, veq_trans, veq_zero_iff, vge_of_veq, not_vlt, refl, rfl, trans, trans', trans_vlt, vle_add, vle_add_cases, vle_div_iff, vle_mul_cancel, vle_mul_left_iff, vle_mul_right, vle_mul_right_iff, vle_of_veq, vle_refl, vle_rfl, vle_total, vle_trans, vle_trans', vle_zero_iff, ne_zero, not_vle, trans, trans_vle, vle, vlt_mul_left, vlt_mul_left_iff, vlt_mul_right, vlt_mul_right_iff, vlt_of_vle_of_vlt, vlt_of_vlt_of_vle, zero_rel, zero_srel_coe_posSubmonoid, zero_srel_iff, zero_srel_mul, zero_srel_one, zero_veq_iff, zero_vle, zero_vlt_coe_posSubmonoid, zero_vlt_iff, zero_vlt_mul, zero_vlt_one
227
Total271

IsValuativeTopology

Theorems

NameKindAssumesProvesValidatesDepends On
mem_nhds_iff πŸ“–mathematicalβ€”Set
Filter
Filter.instMembership
nhds
Set.instHasSubset
Set.image
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
setOf
ValuativeRel.ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
ValuativeRel.valuation
Units.val
MonoidWithZero.toMonoid
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
β€”β€”

Valuation

Definitions

NameCategoryTheorems
Compatible πŸ“–CompData
6 mathmath: Padic.instCompatibleWithZeroMultiplicativeIntMulValuation, WithVal.instCompatibleValuation, Compatible.ofValuation, ValuativeExtension.compatible_comap, ValuativeRel.instCompatibleValueGroupWithZeroValuation, IsNonarchimedeanLocalField.instCompatibleValueGroupWithZeroV

Theorems

NameKindAssumesProvesValidatesDepends On
apply_posSubmonoid_ne_zero πŸ“–β€”β€”β€”β€”IsEquiv.eq_zero
ValuativeRel.isEquiv
ValuativeRel.instCompatibleValueGroupWithZeroValuation
apply_posSubmonoid_pos πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”zero_lt_iff
apply_posSubmonoid_ne_zero
one_rel_iff πŸ“–mathematicalβ€”ValuativeRel.vle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
DFunLike.coe
Valuation
instFunLike
β€”one_vle_iff
one_srel_iff πŸ“–mathematicalβ€”ValuativeRel.vlt
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
DFunLike.coe
Valuation
instFunLike
β€”one_vlt_iff
one_vle_iff πŸ“–mathematicalβ€”ValuativeRel.vle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
DFunLike.coe
Valuation
instFunLike
β€”vle_iff_le
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
instValuationClass
one_vlt_iff πŸ“–mathematicalβ€”ValuativeRel.vlt
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
DFunLike.coe
Valuation
instFunLike
β€”vlt_iff_lt
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
instValuationClass
rel_iff_le πŸ“–mathematicalβ€”ValuativeRel.vle
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
β€”vle_iff_le
rel_one_iff πŸ“–mathematicalβ€”ValuativeRel.vle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
instFunLike
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
β€”vle_one_iff
srel_iff_lt πŸ“–mathematicalβ€”ValuativeRel.vlt
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
β€”vlt_iff_lt
srel_one_iff πŸ“–mathematicalβ€”ValuativeRel.vlt
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
instFunLike
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
β€”vlt_one_iff
veq_iff_eq πŸ“–mathematicalβ€”ValuativeRel.veq
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
β€”vle_iff_le
instReflLe
instAntisymmLe
vle_iff_le πŸ“–mathematicalβ€”ValuativeRel.vle
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
β€”Compatible.vle_iff_le
vle_one_iff πŸ“–mathematicalβ€”ValuativeRel.vle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
instFunLike
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
β€”vle_iff_le
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
instValuationClass
vlt_iff_lt πŸ“–mathematicalβ€”ValuativeRel.vlt
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
β€”β€”
vlt_one_iff πŸ“–mathematicalβ€”ValuativeRel.vlt
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
instFunLike
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
LinearOrderedCommMonoidWithZero.toCommMonoidWithZero
β€”vlt_iff_lt
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
instValuationClass

Valuation.Compatible

Theorems

NameKindAssumesProvesValidatesDepends On
ofValuation πŸ“–mathematicalβ€”Valuation.Compatible
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
ValuativeRel.ofValuation
β€”β€”
srel_iff_lt πŸ“–mathematicalβ€”ValuativeRel.vlt
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
Valuation.instFunLike
β€”Valuation.vlt_iff_lt
vle_iff_le πŸ“–mathematicalβ€”ValuativeRel.vle
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
Valuation.instFunLike
β€”β€”

ValuativeExtension

Definitions

NameCategoryTheorems
mapPosSubmonoid πŸ“–CompOp
2 mathmath: mapValueGroupWithZero_mk, mapPosSubmonoid_apply_coe
mapValueGroupWithZero πŸ“–CompOp
3 mathmath: mapValueGroupWithZero_mk, mapValueGroupWithZero_strictMono, mapValueGroupWithZero_valuation

Theorems

NameKindAssumesProvesValidatesDepends On
compatible_comap πŸ“–mathematicalβ€”Valuation.Compatible
Valuation.comap
CommRing.toRing
algebraMap
CommRing.toCommSemiring
CommSemiring.toSemiring
β€”vle_iff_vle
Valuation.Compatible.vle_iff_le
mapPosSubmonoid_apply_coe πŸ“–mathematicalβ€”Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Submonoid.toMulOneClass
MonoidHom.instFunLike
mapPosSubmonoid
RingHom
RingHom.instFunLike
algebraMap
β€”β€”
mapValueGroupWithZero_mk πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
ValuativeRel.ValueGroupWithZero
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
MonoidWithZeroHom.funLike
mapValueGroupWithZero
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
algebraMap
MonoidHom
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
MulOneClass.toMulOne
Submonoid.toMulOneClass
MonoidHom.instFunLike
mapPosSubmonoid
β€”ValuativeRel.ValueGroupWithZero.mk_eq_div
mapValueGroupWithZero_strictMono πŸ“–mathematicalβ€”StrictMono
ValuativeRel.ValueGroupWithZero
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
MonoidWithZeroHom.funLike
mapValueGroupWithZero
β€”ValuativeRel.ValueGroupWithZero.embed_strictMono
compatible_comap
ValuativeRel.instCompatibleValueGroupWithZeroValuation
mapValueGroupWithZero_valuation πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
ValuativeRel.ValueGroupWithZero
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
MonoidWithZeroHom.funLike
mapValueGroupWithZero
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
ValuativeRel.valuation
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
algebraMap
β€”map_one
MonoidHomClass.toOneHomClass
MonoidHom.instMonoidHomClass
srel_iff_srel πŸ“–mathematicalβ€”ValuativeRel.vlt
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
algebraMap
β€”vlt_iff_vlt
vle_iff_vle πŸ“–mathematicalβ€”ValuativeRel.vle
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
algebraMap
β€”β€”
vlt_iff_vlt πŸ“–mathematicalβ€”ValuativeRel.vlt
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
algebraMap
β€”ValuativeRel.not_vle
vle_iff_vle

ValuativePreorder

Theorems

NameKindAssumesProvesValidatesDepends On
vle_iff_le πŸ“–mathematicalβ€”ValuativeRel.vle
Preorder.toLE
β€”β€”

ValuativeRel

Definitions

NameCategoryTheorems
IsDiscrete πŸ“–CompData
4 mathmath: nonempty_orderIso_withZeroMul_int_iff, IsDiscrete.of_compatible_withZeroMulInt, IsNonarchimedeanLocalField.instIsDiscrete, isDiscrete_trivialRel
IsNontrivial πŸ“–CompData
7 mathmath: isNontrivial_of_rankOne, nonempty_orderIso_withZeroMul_int_iff, isNontrivial_iff_isNontrivial, Padic.instIsNontrivial, isNontrivial_iff_nontrivial_units, not_isNontrivial_of_trivialRel, IsNonarchimedeanLocalField.toIsNontrivial
IsRankLeOne πŸ“–CompData
6 mathmath: IsNonarchimedeanLocalField.instIsRankLeOne, isRankLeOne_iff_mulArchimedean, isRankLeOne_of_rankOne, Padic.instIsRankLeOne, IsRankLeOne.of_compatible_mulArchimedean, IsRankLeOne.of_valuativeExtension
RankLeOneStruct πŸ“–CompData
1 mathmath: IsRankLeOne.nonempty
SRel πŸ“–MathDefβ€”
ValueGroupWithZero πŸ“–CompOp
65 mathmath: ValueGroupWithZero.mk_one_one, ValueGroupWithZero.mk_eq_one, valuation_eq_zero_iff, IsNonarchimedeanLocalField.instIsDiscreteValuationRingSubtypeMemSubringIntegerValueGroupWithZeroValuation, ValueGroupWithZero.mk_pos, supp_eq_valuation_supp, ValueGroupWithZero.embed_strictMono, subsingleton_units_valueGroupWithZero_of_trivialRel, ValueGroupWithZero.mk_eq_div, ValuativeExtension.mapValueGroupWithZero_mk, nonempty_orderIso_withZeroMul_int_iff, IsValuativeTopology.isOpen_ball, ValuativeExtension.mapValueGroupWithZero_strictMono, IsValuativeTopology.isClopen_sphere, ValueGroupWithZero.lift_mul, IsDiscrete.has_maximal_element, ValueGroupWithZero.bot_eq_zero, IsValuativeTopology.continuous_valuation, IsValuativeTopology.mem_nhds_iff', ValueGroupWithZero.inv_mk, exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, ValuativeExtension.mapValueGroupWithZero_valuation, ValueGroupWithZero.mk_lt_mk, IsValuativeTopology.isClosed_closedBall, IsValuativeTopology.mem_nhds_zero_iff, ValueGroupWithZero.mk_mul_mk, IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation, RankLeOneStruct.strictMono, IsNonarchimedeanLocalField.instCompactSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds_zero', isRankLeOne_iff_mulArchimedean, instIsOrderedMonoidValueGroupWithZero, uniformizer_inv_le_iff, IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, IsValuativeTopology.hasBasis_nhds_zero, IsValuativeTopology.isOpen_closedBall, IsNontrivial.exists_lt_one, le_uniformizer_iff, exists_valuation_div_valuation_eq, instCompatibleValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds', isNontrivial_iff_nontrivial_units, IsNonarchimedeanLocalField.isCompact_closedBall, valuation_surjective, ValueGroupWithZero.embed_mk, IsValuativeTopology.isClosed_ball, ValueGroupWithZero.mk_eq_zero, IsValuativeTopology.v_eq_valuation, ValueGroupWithZero.mk_zero, IsNonarchimedeanLocalField.instCompatibleValueGroupWithZeroV, ValueGroupWithZero.mk_le_mk, ValueGroupWithZero.lift_zero, ValueGroupWithZero.mk_self, ValueGroupWithZero.lift_valuation, ValueGroupWithZero.lift_one, IsNonarchimedeanLocalField.instCompleteSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.mem_nhds_iff, uniformizer_lt_one, uniformizer_pos, ValueGroupWithZero.embed_valuation, IsValuativeTopology.isOpen_sphere, instMulArchimedeanValueGroupWithZeroOfIsRankLeOne, ValueGroupWithZero.mk_eq_valuation, IsValuativeTopology.isClopen_closedBall
WithPreorder πŸ“–CompOp
1 mathmath: instValuativePreorderWithPreorder
instBotValueGroupWithZero πŸ“–CompOp
1 mathmath: ValueGroupWithZero.bot_eq_zero
instCommMonoidWithZeroValueGroupWithZero πŸ“–CompOp
4 mathmath: nonempty_orderIso_withZeroMul_int_iff, isRankLeOne_iff_mulArchimedean, instIsOrderedMonoidValueGroupWithZero, instMulArchimedeanValueGroupWithZeroOfIsRankLeOne
instCommRingWithPreorder πŸ“–CompOp
1 mathmath: instValuativePreorderWithPreorder
instInvValueGroupWithZero πŸ“–CompOp
2 mathmath: ValueGroupWithZero.inv_mk, uniformizer_inv_le_iff
instLEValueGroupWithZero πŸ“–CompOp
8 mathmath: IsDiscrete.has_maximal_element, IsValuativeTopology.isClosed_closedBall, uniformizer_inv_le_iff, IsValuativeTopology.isOpen_closedBall, le_uniformizer_iff, IsNonarchimedeanLocalField.isCompact_closedBall, ValueGroupWithZero.mk_le_mk, IsValuativeTopology.isClopen_closedBall
instLinearOrderValueGroupWithZero πŸ“–CompOp
25 mathmath: ValueGroupWithZero.mk_pos, ValueGroupWithZero.embed_strictMono, nonempty_orderIso_withZeroMul_int_iff, IsValuativeTopology.isOpen_ball, ValuativeExtension.mapValueGroupWithZero_strictMono, IsDiscrete.has_maximal_element, IsValuativeTopology.mem_nhds_iff', ValueGroupWithZero.mk_lt_mk, IsValuativeTopology.mem_nhds_zero_iff, RankLeOneStruct.strictMono, IsValuativeTopology.hasBasis_nhds_zero', isRankLeOne_iff_mulArchimedean, instIsOrderedMonoidValueGroupWithZero, uniformizer_inv_le_iff, IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, IsValuativeTopology.hasBasis_nhds_zero, IsNontrivial.exists_lt_one, le_uniformizer_iff, IsValuativeTopology.hasBasis_nhds', IsValuativeTopology.isClosed_ball, IsValuativeTopology.mem_nhds_iff, uniformizer_lt_one, uniformizer_pos, instMulArchimedeanValueGroupWithZeroOfIsRankLeOne
instLinearOrderedCommGroupWithZeroValueGroupWithZero πŸ“–CompOp
41 mathmath: valuation_eq_zero_iff, IsNonarchimedeanLocalField.instIsDiscreteValuationRingSubtypeMemSubringIntegerValueGroupWithZeroValuation, supp_eq_valuation_supp, ValueGroupWithZero.embed_strictMono, subsingleton_units_valueGroupWithZero_of_trivialRel, ValueGroupWithZero.mk_eq_div, ValuativeExtension.mapValueGroupWithZero_mk, IsValuativeTopology.isOpen_ball, ValuativeExtension.mapValueGroupWithZero_strictMono, IsValuativeTopology.isClopen_sphere, IsValuativeTopology.continuous_valuation, IsValuativeTopology.mem_nhds_iff', exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, ValuativeExtension.mapValueGroupWithZero_valuation, IsValuativeTopology.isClosed_closedBall, IsValuativeTopology.mem_nhds_zero_iff, IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation, RankLeOneStruct.strictMono, IsNonarchimedeanLocalField.instCompactSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds_zero', IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, IsValuativeTopology.hasBasis_nhds_zero, IsValuativeTopology.isOpen_closedBall, exists_valuation_div_valuation_eq, instCompatibleValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds', isNontrivial_iff_nontrivial_units, IsNonarchimedeanLocalField.isCompact_closedBall, valuation_surjective, ValueGroupWithZero.embed_mk, IsValuativeTopology.isClosed_ball, IsValuativeTopology.v_eq_valuation, IsNonarchimedeanLocalField.instCompatibleValueGroupWithZeroV, ValueGroupWithZero.lift_valuation, IsNonarchimedeanLocalField.instCompleteSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.mem_nhds_iff, ValueGroupWithZero.embed_valuation, IsValuativeTopology.isOpen_sphere, ValueGroupWithZero.mk_eq_valuation, IsValuativeTopology.isClopen_closedBall
instMulValueGroupWithZero πŸ“–CompOp
3 mathmath: nonempty_orderIso_withZeroMul_int_iff, ValueGroupWithZero.lift_mul, ValueGroupWithZero.mk_mul_mk
instOneValueGroupWithZero πŸ“–CompOp
9 mathmath: ValueGroupWithZero.mk_one_one, ValueGroupWithZero.mk_eq_one, IsDiscrete.has_maximal_element, uniformizer_inv_le_iff, IsNontrivial.exists_lt_one, le_uniformizer_iff, ValueGroupWithZero.mk_self, ValueGroupWithZero.lift_one, uniformizer_lt_one
instOrderBotValueGroupWithZero πŸ“–CompOpβ€”
instPreorderWithPreorder πŸ“–CompOp
1 mathmath: instValuativePreorderWithPreorder
instTransVeq πŸ“–CompOpβ€”
instTransVle πŸ“–CompOpβ€”
instWithPreorder πŸ“–CompOp
1 mathmath: instValuativePreorderWithPreorder
instZeroValueGroupWithZero πŸ“–CompOp
10 mathmath: valuation_eq_zero_iff, ValueGroupWithZero.mk_pos, ValueGroupWithZero.bot_eq_zero, IsValuativeTopology.hasBasis_nhds_zero', IsNontrivial.exists_lt_one, IsValuativeTopology.hasBasis_nhds', ValueGroupWithZero.mk_eq_zero, ValueGroupWithZero.mk_zero, ValueGroupWithZero.lift_zero, uniformizer_pos
ofValuation πŸ“–CompOp
2 mathmath: Valuation.Compatible.ofValuation, trivialRel_eq_ofValuation_one
posSubmonoid πŸ“–CompOp
26 mathmath: ValueGroupWithZero.mk_one_one, ValueGroupWithZero.mk_eq_one, zero_srel_coe_posSubmonoid, ValueGroupWithZero.mk_eq_div, ValueGroupWithZero.exact, ValuativeExtension.mapValueGroupWithZero_mk, ValueGroupWithZero.inv_mk, exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, ValueGroupWithZero.mk_eq_mk, ValueGroupWithZero.mk_lt_mk, Valuation.apply_posSubmonoid_pos, ValueGroupWithZero.mk_mul_mk, zero_vlt_coe_posSubmonoid, one_apply_posSubmonoid, left_cancel_posSubmonoid, exists_valuation_div_valuation_eq, right_cancel_posSubmonoid, ValueGroupWithZero.embed_mk, posSubmonoid_def, ValuativeExtension.mapPosSubmonoid_apply_coe, ValueGroupWithZero.mk_le_mk, ValueGroupWithZero.lift_zero, ValueGroupWithZero.mk_self, ValueGroupWithZero.lift_valuation, ValueGroupWithZero.lift_one, ValueGroupWithZero.mk_eq_valuation
supp πŸ“–CompOp
3 mathmath: supp_eq_valuation_supp, supp_def, instIsPrimeSupp
uniformizer πŸ“–CompOp
4 mathmath: uniformizer_inv_le_iff, le_uniformizer_iff, uniformizer_lt_one, uniformizer_pos
valuation πŸ“–CompOp
33 mathmath: valuation_eq_zero_iff, IsNonarchimedeanLocalField.instIsDiscreteValuationRingSubtypeMemSubringIntegerValueGroupWithZeroValuation, supp_eq_valuation_supp, ValueGroupWithZero.mk_eq_div, IsValuativeTopology.isOpen_ball, IsValuativeTopology.isClopen_sphere, IsValuativeTopology.continuous_valuation, IsValuativeTopology.mem_nhds_iff', exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, ValuativeExtension.mapValueGroupWithZero_valuation, IsValuativeTopology.isClosed_closedBall, IsValuativeTopology.mem_nhds_zero_iff, IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsNonarchimedeanLocalField.instCompactSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds_zero', IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, IsValuativeTopology.hasBasis_nhds_zero, IsValuativeTopology.isOpen_closedBall, exists_valuation_div_valuation_eq, instCompatibleValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds', IsNonarchimedeanLocalField.isCompact_closedBall, valuation_surjective, IsValuativeTopology.isClosed_ball, IsValuativeTopology.v_eq_valuation, ValueGroupWithZero.lift_valuation, IsNonarchimedeanLocalField.instCompleteSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.mem_nhds_iff, ValueGroupWithZero.embed_valuation, IsValuativeTopology.isOpen_sphere, ValueGroupWithZero.mk_eq_valuation, IsValuativeTopology.isClopen_closedBall
valueSetoid πŸ“–CompOpβ€”
veq πŸ“–MathDef
11 mathmath: zero_veq_iff, instSymmVeq, veq_refl, Valuation.veq_iff_eq, veq_comm, instReflVeq, veq_zero_iff, veq.rfl, veq.refl, veq_rfl, veq_def
vle πŸ“–MathDef
70 mathmath: ValueGroupWithZero.mk_eq_one, valuation_eq_zero_iff, srel_iff, vge_of_veq, vle.rfl, vle_mul_left_iff, vle.refl, ValueGroupWithZero.exact, rel_add_cases, vle_refl, vle_add_cases, mul_vle_mul_iff_left, zero_rel, div_vle_one_iff, one_rel_inv, div_vle_iff, supp_def, not_vlt, ValuativePreorder.vle_iff_le, rel_total, one_vle_div_iff, rel_zero_iff, one_rel_div_iff, ValueGroupWithZero.mk_eq_mk, mul_rel_mul_iff_left, ValuativeExtension.vle_iff_vle, Valuation.vle_iff_le, ext_iff, mul_vle_mul_iff_right, SRel.rel, Rel.rfl, instReflVle, inv_rel_one, vle_zero_iff, Valuation.one_vle_iff, left_cancel_posSubmonoid, rel_mul_left_iff, not_vle_one_zero, veq.vge, zero_vle, vlt.not_vle, div_rel_one_iff, Valuation.vle_one_iff, rel_mul_right_iff, veq.vle, vle_div_iff, right_cancel_posSubmonoid, Valuation.rel_one_iff, rel_refl, one_vle_inv, not_srel_iff, rel_rfl, div_rel_iff, ValueGroupWithZero.mk_eq_zero, vle_rfl, Valuation.rel_iff_le, vle_mul_right_iff, inv_vle_one, not_rel_one_zero, ValueGroupWithZero.mk_le_mk, Valuation.Compatible.vle_iff_le, vlt.vle, mul_rel_mul_iff_right, rel_div_iff, vle_of_veq, not_vle, Valuation.one_rel_iff, Rel.refl, veq_def, vle_total
vlt πŸ“–MathDef
32 mathmath: ValuativeExtension.srel_iff_srel, srel_iff, inv_srel_one, zero_srel_coe_posSubmonoid, Valuation.Compatible.srel_iff_lt, ValueGroupWithZero.mk_pos, not_vgt_of_veq, zero_srel_one, not_vlt, not_vlt_zero, ValuativeExtension.vlt_iff_vlt, zero_vlt_one, Valuation.srel_iff_lt, vle.not_vlt, ValueGroupWithZero.mk_lt_mk, Valuation.one_srel_iff, veq.not_vlt, zero_vlt_coe_posSubmonoid, Valuation.one_vlt_iff, one_vlt_inv, Valuation.srel_one_iff, not_vlt_of_veq, Valuation.vlt_one_iff, not_srel_iff, posSubmonoid_def, Valuation.vlt_iff_lt, inv_vlt_one, zero_srel_iff, one_srel_inv, veq.not_vgt, not_vle, zero_vlt_iff
Β«term_<α΅₯_Β» πŸ“–CompOpβ€”
Β«term_=α΅₯_Β» πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
div_rel_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”div_vle_iff
div_rel_one_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
β€”div_vle_one_iff
div_vle_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vle_mul_iff_left
div_mul_cancelβ‚€
div_vle_one_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
β€”div_vle_iff
one_mul
exists_valuation_div_valuation_eq πŸ“–mathematicalβ€”ValueGroupWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
valuation
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
β€”ValueGroupWithZero.ind
div_eq_mul_inv
Subtype.prop
Subtype.coe_eta
mul_one
one_mul
exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq πŸ“–mathematicalβ€”ValueGroupWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
valuation
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
Units.val
MonoidWithZero.toMonoid
GroupWithZero.toMonoidWithZero
β€”exists_valuation_div_valuation_eq
CanLift.prf
Subtype.canLift
Mathlib.Tactic.Contrapose.contrapose₁
valuation_eq_zero_iff
not_vlt
posSubmonoid_def
zero_div
GroupWithZero.toNontrivial
ext πŸ“–β€”vleβ€”β€”β€”
ext_iff πŸ“–mathematicalβ€”vleβ€”ext
instCompatibleValueGroupWithZeroValuation πŸ“–mathematicalβ€”Valuation.Compatible
ValueGroupWithZero
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
valuation
β€”mul_one
instIsNontrivialOfIsNontrivialOfCompatible πŸ“–mathematicalβ€”Valuation.IsNontrivial
CommRing.toRing
β€”isNontrivial_iff_isNontrivial
instIsOrderedMonoidValueGroupWithZero πŸ“–mathematicalβ€”IsOrderedMonoid
ValueGroupWithZero
CommMonoidWithZero.toCommMonoid
instCommMonoidWithZeroValueGroupWithZero
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
β€”ValueGroupWithZero.ind
mul_mul_mul_comm
mul_vle_mul_left
instIsPrimeSupp πŸ“–mathematicalβ€”Ideal.IsPrime
CommSemiring.toSemiring
CommRing.toCommSemiring
supp
β€”supp_eq_valuation_supp
Valuation.instIsPrimeSuppOfNontrivialOfNoZeroDivisors
GroupWithZero.toNontrivial
GroupWithZero.noZeroDivisors
instMulArchimedeanValueGroupWithZeroOfIsRankLeOne πŸ“–mathematicalβ€”MulArchimedean
ValueGroupWithZero
CommMonoidWithZero.toCommMonoid
instCommMonoidWithZeroValueGroupWithZero
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
β€”IsRankLeOne.nonempty
MulArchimedean.comap
NNReal.instMulArchimedean
instReflVeq πŸ“–mathematicalβ€”veqβ€”veq_rfl
instReflVle πŸ“–mathematicalβ€”vleβ€”vle_rfl
instSymmVeq πŸ“–mathematicalβ€”veqβ€”veq.symm
instValuativePreorderWithPreorder πŸ“–mathematicalβ€”ValuativePreorder
WithPreorder
instCommRingWithPreorder
instWithPreorder
instPreorderWithPreorder
β€”β€”
inv_rel_one πŸ“–mathematicalβ€”vle
Field.toCommRing
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
β€”inv_vle_one
inv_srel_one πŸ“–mathematicalβ€”vlt
Field.toCommRing
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
β€”inv_vlt_one
inv_vle_one πŸ“–mathematicalβ€”vle
Field.toCommRing
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
β€”one_div
div_vle_one_iff
inv_vlt_one πŸ“–mathematicalβ€”vlt
Field.toCommRing
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
β€”Iff.not
one_vle_inv
isEquiv πŸ“–mathematicalβ€”Valuation.IsEquiv
CommRing.toRing
β€”β€”
isNontrivial_iff_isNontrivial πŸ“–mathematicalβ€”IsNontrivial
Valuation.IsNontrivial
CommRing.toRing
β€”ValueGroupWithZero.ind
Valuation.Compatible.vle_iff_le
map_zero
MonoidWithZeroHomClass.toZeroHomClass
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
Iff.ne
Valuation.IsEquiv.eq_zero
isEquiv
instCompatibleValueGroupWithZeroValuation
Valuation.IsEquiv.eq_one_iff_eq_one
isNontrivial_iff_nontrivial_units πŸ“–mathematicalβ€”IsNontrivial
Nontrivial
Units
ValueGroupWithZero
MonoidWithZero.toMonoid
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
β€”eq_or_ne
GroupWithZero.toNontrivial
le_uniformizer_iff πŸ“–mathematicalβ€”ValueGroupWithZero
instLEValueGroupWithZero
uniformizer
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
instOneValueGroupWithZero
β€”LE.le.trans_lt
uniformizer_lt_one
IsDiscrete.has_maximal_element
left_cancel_posSubmonoid πŸ“–mathematicalβ€”vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
β€”β€”
mul_rel_mul πŸ“–mathematicalvleDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vle_mul
mul_rel_mul_iff_left πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vle_mul_iff_left
mul_rel_mul_iff_right πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vle_mul_iff_right
mul_srel_mul πŸ“–mathematicalvltDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vlt_mul
mul_srel_mul_iff_left πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_left
mul_srel_mul_iff_right πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_right
mul_srel_mul_of_rel_of_srel πŸ“–mathematicalvle
vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_of_vle_of_vlt
mul_srel_mul_of_srel_of_rel πŸ“–mathematicalvlt
vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_of_vlt_of_vle
mul_veq_mul πŸ“–mathematicalveqDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vle_mul
veq.vle
veq.vge
mul_vle_mul πŸ“–mathematicalvleDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”vle.trans
mul_vle_mul_left
mul_vle_mul_right
mul_vle_mul_iff_left πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”vle_mul_cancel
mul_vle_mul_left
mul_vle_mul_iff_right πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_comm
mul_vle_mul_left πŸ“–mathematicalvleDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”β€”
mul_vle_mul_right πŸ“–mathematicalvleDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_comm
mul_vle_mul_left
mul_vlt_mul πŸ“–mathematicalvltDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”vle.trans_vlt
mul_vle_mul_right
vlt.vle
mul_vlt_mul_left
zero_vle
mul_vlt_mul_iff_left πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Iff.not
mul_vle_mul_iff_left
mul_vlt_mul_iff_right πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Iff.not
mul_vle_mul_iff_right
mul_vlt_mul_left πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_left
mul_vlt_mul_of_vle_of_vlt πŸ“–mathematicalvle
vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”vlt.trans_vle
mul_vlt_mul_right
mul_vle_mul_left
mul_vlt_mul_of_vlt_of_vle πŸ“–mathematicalvlt
vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”vle.trans_vlt
mul_vle_mul_right
mul_vlt_mul_left
mul_vlt_mul_right πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_right
not_rel_one_zero πŸ“–mathematicalβ€”vle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”not_vle_one_zero
not_srel_iff πŸ“–mathematicalβ€”vlt
vle
β€”not_vlt
not_vgt_of_veq πŸ“–mathematicalveqvltβ€”vle.not_vlt
veq.vle
not_vle πŸ“–mathematicalβ€”vle
vlt
β€”β€”
not_vle_one_zero πŸ“–mathematicalβ€”vle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”β€”
not_vlt πŸ“–mathematicalβ€”vlt
vle
β€”Iff.not_left
not_vle
not_vlt_of_veq πŸ“–mathematicalveqvltβ€”vle.not_vlt
veq.vge
not_vlt_zero πŸ“–mathematicalβ€”vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”β€”
one_apply_posSubmonoid πŸ“–mathematicalβ€”DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Valuation.one
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
LinearOrderedCommGroupWithZero.toCommGroupWithZero
β€”Valuation.one_apply_of_ne_zero
one_rel_div_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
β€”one_vle_div_iff
one_rel_inv πŸ“–mathematicalβ€”vle
Field.toCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
β€”one_vle_inv
one_srel_inv πŸ“–mathematicalβ€”vlt
Field.toCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
β€”one_vlt_inv
one_vle_div_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
β€”vle_div_iff
one_mul
one_vle_inv πŸ“–mathematicalβ€”vle
Field.toCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
β€”one_div
one_vle_div_iff
one_vlt_inv πŸ“–mathematicalβ€”vlt
Field.toCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
β€”Iff.not
inv_vle_one
posSubmonoid_def πŸ“–mathematicalβ€”Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”β€”
pow_rel_pow πŸ“–mathematicalvleMonoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”pow_vle_pow
pow_rel_pow_of_one_rel πŸ“–mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”pow_vle_pow_of_one_vle
pow_rel_pow_of_rel_one πŸ“–mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”pow_vle_pow_of_vle_one
pow_srel_pow πŸ“–mathematicalvltMonoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”pow_vlt_pow
pow_vle_pow πŸ“–mathematicalvleMonoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”pow_zero
pow_succ
mul_vle_mul
pow_vle_pow_of_one_vle πŸ“–mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”ExistsAddOfLE.exists_add_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
Nat.instCanonicallyOrderedAdd
pow_add
one_pow
mul_one
mul_vle_mul_right
pow_vle_pow
pow_vle_pow_of_vle_one πŸ“–mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”ExistsAddOfLE.exists_add_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
Nat.instCanonicallyOrderedAdd
pow_add
one_pow
mul_one
mul_vle_mul_right
pow_vle_pow
pow_vlt_pow πŸ“–mathematicalvltMonoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”pow_one
pow_succ
rel_add πŸ“–mathematicalvleDistrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”vle_add
rel_add_cases πŸ“–mathematicalβ€”vle
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”vle_add_cases
rel_div_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”vle_div_iff
rel_mul πŸ“–mathematicalvleDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vle_mul
rel_mul_cancel πŸ“–β€”vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”β€”vle_mul_cancel
rel_mul_left πŸ“–mathematicalvleDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vle_mul_right
rel_mul_left_iff πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vle_mul_iff_right
rel_mul_right πŸ“–mathematicalvleDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vle_mul_left
rel_mul_right_iff πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”vle_mul_right_iff
rel_refl πŸ“–mathematicalβ€”vleβ€”vle_refl
rel_rfl πŸ“–mathematicalβ€”vleβ€”vle_rfl
rel_total πŸ“–mathematicalβ€”vleβ€”vle_total
rel_trans πŸ“–β€”vleβ€”β€”vle_trans
rel_trans' πŸ“–β€”vleβ€”β€”vle_trans'
rel_zero_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”vle_zero_iff
right_cancel_posSubmonoid πŸ“–mathematicalβ€”vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
β€”β€”
srel_iff πŸ“–mathematicalβ€”vlt
vle
β€”β€”
srel_mul_left πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_right
srel_mul_left_iff πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_right
srel_mul_right πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_right
srel_mul_right_iff πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_left
srel_of_rel_of_srel πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_left
srel_of_srel_of_rel πŸ“–β€”vlt
vle
β€”β€”vlt_of_vlt_of_vle
supp_def πŸ“–mathematicalβ€”Ideal
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submodule.setLike
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
supp
vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”β€”
supp_eq_valuation_supp πŸ“–mathematicalβ€”supp
Valuation.supp
ValueGroupWithZero
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
valuation
β€”Ideal.ext
valuation_eq_zero_iff
uniformizer_inv_le_iff πŸ“–mathematicalβ€”ValueGroupWithZero
instLEValueGroupWithZero
instInvValueGroupWithZero
uniformizer
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
instOneValueGroupWithZero
β€”bot_lt_iff_ne_bot
inv_le_commβ‚€
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
LinearOrderedCommMonoidWithZero.toMulPosStrictMono
uniformizer_pos
le_uniformizer_iff
inv_lt_oneβ‚€
uniformizer_lt_one πŸ“–mathematicalβ€”ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
uniformizer
instOneValueGroupWithZero
β€”IsDiscrete.has_maximal_element
uniformizer_ne_zero πŸ“–β€”β€”β€”β€”LT.lt.ne'
uniformizer_pos
uniformizer_pos πŸ“–mathematicalβ€”ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
instZeroValueGroupWithZero
uniformizer
β€”IsNontrivial.exists_lt_one
LT.lt.trans_le
le_uniformizer_iff
val_posSubmonoid_ne_zero πŸ“–β€”β€”β€”β€”Subtype.prop
Mathlib.Tactic.Contrapose.contrapose₃
posSubmonoid_def
valuation_eq_zero_iff πŸ“–mathematicalβ€”DFunLike.coe
Valuation
ValueGroupWithZero
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
valuation
instZeroValueGroupWithZero
vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”ValueGroupWithZero.mk_eq_zero
valuation_posSubmonoid_ne_zero πŸ“–β€”β€”β€”β€”valuation_eq_zero_iff
Subtype.prop
valuation_surjective πŸ“–mathematicalβ€”ValueGroupWithZero
Field.toCommRing
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
valuation
β€”ValueGroupWithZero.ind
ValueGroupWithZero.mk_eq_valuation
veq_comm πŸ“–mathematicalβ€”veqβ€”antisymmRel_comm
veq_def πŸ“–mathematicalβ€”veq
vle
β€”β€”
veq_refl πŸ“–mathematicalβ€”veqβ€”AntisymmRel.rfl
instReflVle
veq_rfl πŸ“–mathematicalβ€”veqβ€”veq_refl
veq_trans πŸ“–β€”veqβ€”β€”AntisymmRel.trans
instIsTransOfTrans
veq_zero_iff πŸ“–mathematicalβ€”veq
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”veq_comm
zero_veq_iff
vge_of_veq πŸ“–mathematicalveqvleβ€”β€”
vle_add πŸ“–mathematicalvleDistrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”β€”
vle_add_cases πŸ“–mathematicalβ€”vle
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”vle_add
vle.rfl
vle_total
vle_div_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vle_mul_iff_left
div_mul_cancelβ‚€
vle_mul_cancel πŸ“–β€”vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”β€”β€”
vle_mul_left_iff πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vle_mul_iff_right
vle_mul_right πŸ“–mathematicalvleDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_vle_mul_left
vle_mul_right_iff πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vle_mul_iff_left
vle_of_veq πŸ“–mathematicalveqvleβ€”β€”
vle_refl πŸ“–mathematicalβ€”vleβ€”vle_total
vle_rfl πŸ“–mathematicalβ€”vleβ€”vle_refl
vle_total πŸ“–mathematicalβ€”vleβ€”β€”
vle_trans πŸ“–β€”vleβ€”β€”β€”
vle_trans' πŸ“–β€”vleβ€”β€”vle.trans
vle_zero_iff πŸ“–mathematicalβ€”vle
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”supp_def
Ideal.eq_bot_of_prime
instIsPrimeSupp
Ideal.mem_bot
vlt_mul_left πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_right
vlt_mul_left_iff πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_right
vlt_mul_right πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_left
vlt_mul_right_iff πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”mul_vlt_mul_iff_left
vlt_of_vle_of_vlt πŸ“–β€”vle
vlt
β€”β€”lt_of_le_of_lt
vlt_of_vlt_of_vle πŸ“–β€”vlt
vle
β€”β€”lt_of_lt_of_le
zero_rel πŸ“–mathematicalβ€”vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”zero_vle
zero_srel_coe_posSubmonoid πŸ“–mathematicalβ€”vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
β€”zero_vlt_coe_posSubmonoid
zero_srel_iff πŸ“–mathematicalβ€”vlt
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”zero_vlt_iff
zero_srel_mul πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”zero_vlt_mul
zero_srel_one πŸ“–mathematicalβ€”vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
β€”zero_vlt_one
zero_veq_iff πŸ“–mathematicalβ€”veq
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”vle_zero_iff
zero_vle πŸ“–mathematicalβ€”vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”MulZeroClass.zero_mul
one_mul
mul_vle_mul_left
vle_total
not_vle_one_zero
zero_vlt_coe_posSubmonoid πŸ“–mathematicalβ€”vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
β€”Subtype.prop
zero_vlt_iff πŸ“–mathematicalβ€”vlt
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”β€”
zero_vlt_mul πŸ“–mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Mathlib.Tactic.Contrapose.contrapose₁
not_vlt
vle_mul_cancel
mul_comm
MulZeroClass.mul_zero
zero_vlt_one πŸ“–mathematicalβ€”vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
β€”not_vle_one_zero

ValuativeRel.IsDiscrete

Theorems

NameKindAssumesProvesValidatesDepends On
has_maximal_element πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
ValuativeRel.instLEValueGroupWithZero
β€”β€”

ValuativeRel.IsNontrivial

Theorems

NameKindAssumesProvesValidatesDepends On
condition πŸ“–β€”β€”β€”β€”β€”
exists_lt_one πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
β€”condition
lt_or_lt_iff_ne
zero_lt_iff
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
LinearOrderedCommMonoidWithZero.toZeroLeOneClass

ValuativeRel.IsRankLeOne

Theorems

NameKindAssumesProvesValidatesDepends On
nonempty πŸ“–mathematicalβ€”ValuativeRel.RankLeOneStructβ€”β€”
of_valuativeExtension πŸ“–mathematicalβ€”ValuativeRel.IsRankLeOneβ€”nonempty
StrictMono.comp
ValuativeExtension.mapValueGroupWithZero_strictMono

ValuativeRel.RankLeOneStruct

Definitions

NameCategoryTheorems
emb πŸ“–CompOp
1 mathmath: strictMono

Theorems

NameKindAssumesProvesValidatesDepends On
strictMono πŸ“–mathematicalβ€”StrictMono
ValuativeRel.ValueGroupWithZero
NNReal
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
instPartialOrderNNReal
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
instSemiringNNReal
MonoidWithZeroHom.funLike
emb
β€”β€”

ValuativeRel.Rel

Theorems

NameKindAssumesProvesValidatesDepends On
refl πŸ“–mathematicalβ€”ValuativeRel.vleβ€”ValuativeRel.vle.refl
rfl πŸ“–mathematicalβ€”ValuativeRel.vleβ€”ValuativeRel.vle.rfl
trans πŸ“–β€”ValuativeRel.vleβ€”β€”ValuativeRel.vle.trans
trans' πŸ“–β€”ValuativeRel.vleβ€”β€”ValuativeRel.vle.trans'
trans_srel πŸ“–mathematicalValuativeRel.vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”ValuativeRel.srel_of_rel_of_srel

ValuativeRel.SRel

Theorems

NameKindAssumesProvesValidatesDepends On
rel πŸ“–mathematicalValuativeRel.vltValuativeRel.vleβ€”ValuativeRel.vlt.vle
trans πŸ“–β€”ValuativeRel.vltβ€”β€”ValuativeRel.vlt.trans
trans_rel πŸ“–β€”ValuativeRel.vlt
ValuativeRel.vle
β€”β€”ValuativeRel.vlt.trans_vle

ValuativeRel.ValueGroupWithZero

Definitions

NameCategoryTheorems
embed πŸ“–CompOp
3 mathmath: embed_strictMono, embed_mk, embed_valuation
liftβ‚‚ πŸ“–CompOp
1 mathmath: liftβ‚‚_mk
mk πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
bot_eq_zero πŸ“–mathematicalβ€”Bot.bot
ValuativeRel.ValueGroupWithZero
ValuativeRel.instBotValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
β€”β€”
embed_mk πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
ValuativeRel.ValueGroupWithZero
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
MonoidWithZeroHom.funLike
embed
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”β€”
embed_strictMono πŸ“–mathematicalβ€”StrictMono
ValuativeRel.ValueGroupWithZero
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
LinearOrderedCommMonoidWithZero.toLinearOrder
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
MonoidWithZeroHom.funLike
embed
β€”ValuativeRel.exists_valuation_div_valuation_eq
map_divβ‚€
MonoidWithZeroHom.monoidWithZeroHomClass
div_lt_div_iffβ‚€
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
GroupWithZero.toNontrivial
ValuativeRel.instCompatibleValueGroupWithZeroValuation
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
div_one
map_mul
MonoidHomClass.toMulHomClass
Valuation.IsEquiv.lt_iff_lt
ValuativeRel.isEquiv
embed_valuation πŸ“–mathematicalβ€”DFunLike.coe
MonoidWithZeroHom
ValuativeRel.ValueGroupWithZero
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
MonoidWithZeroHom.funLike
embed
ValuativeRel.valuation
ValuativeRel.instCompatibleValueGroupWithZeroValuation
β€”ind
ValuativeRel.instCompatibleValueGroupWithZeroValuation
exact πŸ“–mathematicalβ€”ValuativeRel.vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”β€”
ind πŸ“–β€”β€”β€”β€”β€”
inv_mk πŸ“–mathematicalValuativeRel.vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
ValuativeRel.ValueGroupWithZero
ValuativeRel.instInvValueGroupWithZero
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”β€”
lift_mk πŸ“–mathematicalβ€”liftβ€”β€”
lift_mul πŸ“–mathematicalDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
Submonoid.mul
lift
ValuativeRel.ValueGroupWithZero
ValuativeRel.instMulValueGroupWithZero
β€”ind
lift_one πŸ“–mathematicalβ€”lift
ValuativeRel.ValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
Submonoid.one
β€”β€”
lift_valuation πŸ“–mathematicalβ€”lift
DFunLike.coe
Valuation
ValuativeRel.ValueGroupWithZero
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
ValuativeRel.valuation
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
Submonoid.one
β€”β€”
lift_zero πŸ“–mathematicalβ€”lift
ValuativeRel.ValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
Submonoid.one
β€”β€”
liftβ‚‚_mk πŸ“–mathematicalβ€”liftβ‚‚β€”β€”
mk_eq_div πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
ValuativeRel.valuation
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”eq_div_iff
ValuativeRel.valuation_posSubmonoid_ne_zero
mul_one
mk_eq_mk πŸ“–mathematicalβ€”ValuativeRel.vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”Quotient.eq
mk_eq_one πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
ValuativeRel.vle
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”mul_one
one_mul
mk_eq_valuation πŸ“–mathematicalβ€”Field.toCommRing
DFunLike.coe
Valuation
ValuativeRel.ValueGroupWithZero
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
ValuativeRel.valuation
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”Valuation.map_div
mk_eq_div
mk_eq_zero πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
ValuativeRel.vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mul_one
MulZeroClass.zero_mul
sound
mk_le_mk πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
ValuativeRel.instLEValueGroupWithZero
ValuativeRel.vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”β€”
mk_lt_mk πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
ValuativeRel.vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”lt_iff_not_ge
ValuativeRel.not_vle
mk_mul_mk πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
ValuativeRel.instMulValueGroupWithZero
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
Submonoid.mul
β€”β€”
mk_one_one πŸ“–mathematicalβ€”AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
Submonoid.one
ValuativeRel.ValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
β€”sound
mul_one
mk_pos πŸ“–mathematicalβ€”ValuativeRel.ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
ValuativeRel.vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”mk_zero
MulZeroClass.zero_mul
mul_one
mk_self πŸ“–mathematicalβ€”Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
ValuativeRel.ValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
β€”sound
mul_one
one_mul
mk_zero πŸ“–mathematicalβ€”MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
ValuativeRel.ValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
β€”mk_eq_zero
ValuativeRel.vle.rfl
sound πŸ“–β€”ValuativeRel.vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
β€”β€”β€”

ValuativeRel.veq

Theorems

NameKindAssumesProvesValidatesDepends On
not_vgt πŸ“–mathematicalValuativeRel.veqValuativeRel.vltβ€”ValuativeRel.not_vgt_of_veq
not_vlt πŸ“–mathematicalValuativeRel.veqValuativeRel.vltβ€”ValuativeRel.not_vlt_of_veq
refl πŸ“–mathematicalβ€”ValuativeRel.veqβ€”ValuativeRel.veq_refl
rfl πŸ“–mathematicalβ€”ValuativeRel.veqβ€”ValuativeRel.veq_rfl
vge πŸ“–mathematicalValuativeRel.veqValuativeRel.vleβ€”ValuativeRel.vge_of_veq
vle πŸ“–mathematicalValuativeRel.veqValuativeRel.vleβ€”ValuativeRel.vle_of_veq

ValuativeRel.vle

Theorems

NameKindAssumesProvesValidatesDepends On
not_vlt πŸ“–mathematicalValuativeRel.vleValuativeRel.vltβ€”ValuativeRel.not_vlt
refl πŸ“–mathematicalβ€”ValuativeRel.vleβ€”ValuativeRel.vle_refl
rfl πŸ“–mathematicalβ€”ValuativeRel.vleβ€”ValuativeRel.vle_rfl
trans πŸ“–β€”ValuativeRel.vleβ€”β€”ValuativeRel.vle_trans
trans' πŸ“–β€”ValuativeRel.vleβ€”β€”ValuativeRel.vle_trans'
trans_vlt πŸ“–β€”ValuativeRel.vle
ValuativeRel.vlt
β€”β€”ValuativeRel.vlt_of_vle_of_vlt

ValuativeRel.vlt

Theorems

NameKindAssumesProvesValidatesDepends On
ne_zero πŸ“–β€”ValuativeRel.vltβ€”β€”ValuativeRel.not_vlt_zero
not_vle πŸ“–mathematicalValuativeRel.vltValuativeRel.vleβ€”ValuativeRel.not_vle
trans πŸ“–β€”ValuativeRel.vltβ€”β€”trans_vle
vle
trans_vle πŸ“–β€”ValuativeRel.vlt
ValuativeRel.vle
β€”β€”ValuativeRel.vlt_of_vlt_of_vle
vle πŸ“–mathematicalValuativeRel.vltValuativeRel.vleβ€”le_of_lt

(root)

Definitions

NameCategoryTheorems
IsValuativeTopology πŸ“–CompData
2 mathmath: IsValuativeTopology.of_zero, IsNonarchimedeanLocalField.toIsValuativeTopology
ValuativeExtension πŸ“–CompDataβ€”
ValuativePreorder πŸ“–CompData
1 mathmath: ValuativeRel.instValuativePreorderWithPreorder
Β«term_≀α΅₯_Β» πŸ“–CompOpβ€”

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