Documentation Verification Report

Basic

📁 Source: Mathlib/RingTheory/Valuation/ValuativeRel/Basic.lean

Statistics

MetricCount
DefinitionsCompatible, ValuativeExtension, mapPosSubmonoid, mapValueGroupWithZero, ValuativePreorder, IsDiscrete, IsNontrivial, IsRankLeOne, RankLeOneStruct, emb, SRel, ValueGroupWithZero, embed, lift₂, mk, orderMonoidIso, valueGroupWithZero_equiv_valueGroup₀, 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, «term_<ᵥ_», «term_=ᵥ_», «term_≤ᵥ_»
45
TheoremsofValuation, 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_eq_restrict₀, embedding_embed_valuation_eq, embedding_orderMonoidIso_valuation_eq, exact, ind, inv_mk, leftInverse_embedding_orderMonoidIso, lift_mk, lift_mul, lift_one, lift_valuation, lift_zero, lift₂_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, orderMonoidIso_embed, orderMonoidIso_mk, orderMonoidIso_strictMono, orderMonoidIso_valuation_eq_restrict₀, 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, restrict_lt_orderMonoidIso, 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_lt_symm_orderMonoidIso, 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
235
Total280

Valuation

Definitions

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

Theorems

NameKindAssumesProvesValidatesDepends On
apply_posSubmonoid_ne_zero 📖IsEquiv.eq_zero
ValuativeRel.isEquiv
ValuativeRel.instCompatibleValueGroupWithZeroValuation
apply_posSubmonoid_pos 📖mathematicalPreorder.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
zero_lt_iff
apply_posSubmonoid_ne_zero
one_rel_iff 📖mathematicalValuativeRel.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
one_vle_iff
one_srel_iff 📖mathematicalValuativeRel.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
one_vlt_iff
one_vle_iff 📖mathematicalValuativeRel.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
vle_iff_le
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
instValuationClass
one_vlt_iff 📖mathematicalValuativeRel.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
vlt_iff_lt
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
instValuationClass
rel_iff_le 📖mathematicalValuativeRel.vle
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
vle_iff_le
rel_one_iff 📖mathematicalValuativeRel.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
vle_one_iff
srel_iff_lt 📖mathematicalValuativeRel.vlt
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
vlt_iff_lt
srel_one_iff 📖mathematicalValuativeRel.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
vlt_one_iff
veq_iff_eq 📖mathematicalValuativeRel.veq
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
vle_iff_le
instReflLe
instAntisymmLe
vle_iff_le 📖mathematicalValuativeRel.vle
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
Compatible.vle_iff_le
vle_one_iff 📖mathematicalValuativeRel.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
vle_iff_le
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
instValuationClass
vlt_iff_lt 📖mathematicalValuativeRel.vlt
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
instFunLike
vlt_one_iff 📖mathematicalValuativeRel.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
vlt_iff_lt
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
ValuationClass.toMonoidWithZeroHomClass
instValuationClass

Valuation.Compatible

Theorems

NameKindAssumesProvesValidatesDepends On
ofValuation 📖mathematicalValuation.Compatible
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
ValuativeRel.ofValuation
srel_iff_lt 📖mathematicalValuativeRel.vlt
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
Valuation.instFunLike
Valuation.vlt_iff_lt
vle_iff_le 📖mathematicalValuativeRel.vle
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
Valuation
CommRing.toRing
Valuation.instFunLike

ValuativeExtension

Definitions

NameCategoryTheorems
mapPosSubmonoid 📖CompOp
2 mathmath: mapValueGroupWithZero_mk, mapPosSubmonoid_apply_coe
mapValueGroupWithZero 📖CompOp
3 mathmath: mapValueGroupWithZero_mk, mapValueGroupWithZero_strictMono, mapValueGroupWithZero_valuation

Theorems

NameKindAssumesProvesValidatesDepends On
compatible_comap 📖mathematicalValuation.Compatible
Valuation.comap
CommRing.toRing
algebraMap
CommRing.toCommSemiring
CommSemiring.toSemiring
vle_iff_vle
Valuation.Compatible.vle_iff_le
mapPosSubmonoid_apply_coe 📖mathematicalSubmonoid
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
mapValueGroupWithZero_mk 📖mathematicalDFunLike.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
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
map_div₀
MonoidWithZeroHom.monoidWithZeroHomClass
MonoidWithZeroHom.ValueGroup₀.embedding_restrict₀
ValuativeRel.ValueGroupWithZero.mk_eq_div
mapValueGroupWithZero_strictMono 📖mathematicalStrictMono
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
StrictMono.comp
MonoidWithZeroHom.monoidWithZeroHomClass
MonoidWithZeroHom.ValueGroup₀.embedding_strictMono
ValuativeRel.ValueGroupWithZero.embed_strictMono
compatible_comap
ValuativeRel.instCompatibleValueGroupWithZeroValuation
mapValueGroupWithZero_valuation 📖mathematicalDFunLike.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
map_one
MonoidHomClass.toOneHomClass
MonoidHom.instMonoidHomClass
srel_iff_srel 📖mathematicalValuativeRel.vlt
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
algebraMap
vlt_iff_vlt
vle_iff_vle 📖mathematicalValuativeRel.vle
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
algebraMap
vlt_iff_vlt 📖mathematicalValuativeRel.vlt
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
algebraMap
ValuativeRel.not_vle
vle_iff_vle

ValuativePreorder

Theorems

NameKindAssumesProvesValidatesDepends On
vle_iff_le 📖mathematicalValuativeRel.vle
Preorder.toLE

ValuativeRel

Definitions

NameCategoryTheorems
IsDiscrete 📖CompData
4 mathmath: nonempty_orderIso_withZeroMul_int_iff, IsDiscrete.of_compatible_withZeroMulInt, IsNonarchimedeanLocalField.instIsDiscrete, isDiscrete_trivialRel
IsNontrivial 📖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 📖CompData
6 mathmath: IsNonarchimedeanLocalField.instIsRankLeOne, isRankLeOne_iff_mulArchimedean, isRankLeOne_of_rankOne, Padic.instIsRankLeOne, IsRankLeOne.of_compatible_mulArchimedean, IsRankLeOne.of_valuativeExtension
RankLeOneStruct 📖CompData
1 mathmath: IsRankLeOne.nonempty
SRel 📖MathDef
ValueGroupWithZero 📖CompOp
68 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, ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀, nonempty_orderIso_withZeroMul_int_iff, ValueGroupWithZero.leftInverse_embedding_orderMonoidIso, ValuativeExtension.mapValueGroupWithZero_strictMono, ValueGroupWithZero.lift_mul, IsDiscrete.has_maximal_element, IsNontrivial.condition, 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.embed_valuation_eq_restrict₀, ValueGroupWithZero.orderMonoidIso_mk, ValueGroupWithZero.mk_lt_mk, IsValuativeTopology.mem_nhds_zero_iff, ValueGroupWithZero.orderMonoidIso_embed, ValueGroupWithZero.mk_mul_mk, IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation, RankLeOneStruct.strictMono, IsNonarchimedeanLocalField.instCompactSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds_zero', isRankLeOne_iff_mulArchimedean, instIsOrderedMonoidValueGroupWithZero, uniformizer_inv_le_iff, IsValuativeTopology.hasBasis_nhds, IsValuativeTopology.hasBasis_nhds_zero, 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, ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq, ValueGroupWithZero.mk_eq_zero, IsValuativeTopology.v_eq_valuation, ValueGroupWithZero.mk_zero, valuation_lt_symm_orderMonoidIso, IsNonarchimedeanLocalField.instCompatibleValueGroupWithZeroV, ValueGroupWithZero.mk_le_mk, ValueGroupWithZero.lift_zero, ValueGroupWithZero.embedding_embed_valuation_eq, ValueGroupWithZero.mk_self, restrict_lt_orderMonoidIso, ValueGroupWithZero.lift_valuation, ValueGroupWithZero.lift_one, IsNonarchimedeanLocalField.instCompleteSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.mem_nhds_iff, Valuation.exists_setOf_restrict_le_iff, ValueGroupWithZero.orderMonoidIso_strictMono, uniformizer_lt_one, uniformizer_pos, instMulArchimedeanValueGroupWithZeroOfIsRankLeOne, ValueGroupWithZero.mk_eq_valuation
WithPreorder 📖CompOp
1 mathmath: instValuativePreorderWithPreorder
instBotValueGroupWithZero 📖CompOp
1 mathmath: ValueGroupWithZero.bot_eq_zero
instCommMonoidWithZeroValueGroupWithZero 📖CompOp
4 mathmath: nonempty_orderIso_withZeroMul_int_iff, isRankLeOne_iff_mulArchimedean, instIsOrderedMonoidValueGroupWithZero, instMulArchimedeanValueGroupWithZeroOfIsRankLeOne
instCommRingWithPreorder 📖CompOp
1 mathmath: instValuativePreorderWithPreorder
instInvValueGroupWithZero 📖CompOp
2 mathmath: ValueGroupWithZero.inv_mk, uniformizer_inv_le_iff
instLEValueGroupWithZero 📖CompOp
5 mathmath: IsDiscrete.has_maximal_element, uniformizer_inv_le_iff, le_uniformizer_iff, IsNonarchimedeanLocalField.isCompact_closedBall, ValueGroupWithZero.mk_le_mk
instLinearOrderValueGroupWithZero 📖CompOp
30 mathmath: ValueGroupWithZero.mk_pos, ValueGroupWithZero.embed_strictMono, ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀, nonempty_orderIso_withZeroMul_int_iff, ValueGroupWithZero.leftInverse_embedding_orderMonoidIso, ValuativeExtension.mapValueGroupWithZero_strictMono, IsDiscrete.has_maximal_element, IsValuativeTopology.mem_nhds_iff', ValueGroupWithZero.orderMonoidIso_mk, ValueGroupWithZero.mk_lt_mk, IsValuativeTopology.mem_nhds_zero_iff, RankLeOneStruct.strictMono, IsValuativeTopology.hasBasis_nhds_zero', isRankLeOne_iff_mulArchimedean, instIsOrderedMonoidValueGroupWithZero, uniformizer_inv_le_iff, IsValuativeTopology.hasBasis_nhds, IsValuativeTopology.hasBasis_nhds_zero, IsNontrivial.exists_lt_one, le_uniformizer_iff, IsValuativeTopology.hasBasis_nhds', ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq, valuation_lt_symm_orderMonoidIso, restrict_lt_orderMonoidIso, IsValuativeTopology.mem_nhds_iff, Valuation.exists_setOf_restrict_le_iff, ValueGroupWithZero.orderMonoidIso_strictMono, uniformizer_lt_one, uniformizer_pos, instMulArchimedeanValueGroupWithZeroOfIsRankLeOne
instLinearOrderedCommGroupWithZeroValueGroupWithZero 📖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, ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀, ValueGroupWithZero.leftInverse_embedding_orderMonoidIso, ValuativeExtension.mapValueGroupWithZero_strictMono, IsValuativeTopology.continuous_valuation, IsValuativeTopology.mem_nhds_iff', exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, ValuativeExtension.mapValueGroupWithZero_valuation, ValueGroupWithZero.embed_valuation_eq_restrict₀, IsValuativeTopology.mem_nhds_zero_iff, ValueGroupWithZero.orderMonoidIso_embed, IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation, RankLeOneStruct.strictMono, IsNonarchimedeanLocalField.instCompactSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds_zero', IsValuativeTopology.hasBasis_nhds, IsValuativeTopology.hasBasis_nhds_zero, exists_valuation_div_valuation_eq, instCompatibleValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds', isNontrivial_iff_nontrivial_units, IsNonarchimedeanLocalField.isCompact_closedBall, valuation_surjective, ValueGroupWithZero.embed_mk, ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq, IsValuativeTopology.v_eq_valuation, valuation_lt_symm_orderMonoidIso, IsNonarchimedeanLocalField.instCompatibleValueGroupWithZeroV, ValueGroupWithZero.embedding_embed_valuation_eq, restrict_lt_orderMonoidIso, ValueGroupWithZero.lift_valuation, IsNonarchimedeanLocalField.instCompleteSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.mem_nhds_iff, Valuation.exists_setOf_restrict_le_iff, ValueGroupWithZero.mk_eq_valuation
instMulValueGroupWithZero 📖CompOp
10 mathmath: ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀, nonempty_orderIso_withZeroMul_int_iff, ValueGroupWithZero.leftInverse_embedding_orderMonoidIso, ValueGroupWithZero.lift_mul, ValueGroupWithZero.orderMonoidIso_mk, ValueGroupWithZero.mk_mul_mk, ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq, valuation_lt_symm_orderMonoidIso, restrict_lt_orderMonoidIso, ValueGroupWithZero.orderMonoidIso_strictMono
instOneValueGroupWithZero 📖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 📖CompOp
instPreorderWithPreorder 📖CompOp
1 mathmath: instValuativePreorderWithPreorder
instTransVeq 📖CompOp
instTransVle 📖CompOp
instWithPreorder 📖CompOp
1 mathmath: instValuativePreorderWithPreorder
instZeroValueGroupWithZero 📖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 📖CompOp
2 mathmath: Valuation.Compatible.ofValuation, trivialRel_eq_ofValuation_one
posSubmonoid 📖CompOp
27 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.orderMonoidIso_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 📖CompOp
3 mathmath: supp_eq_valuation_supp, supp_def, instIsPrimeSupp
uniformizer 📖CompOp
4 mathmath: uniformizer_inv_le_iff, le_uniformizer_iff, uniformizer_lt_one, uniformizer_pos
valuation 📖CompOp
32 mathmath: valuation_eq_zero_iff, IsNonarchimedeanLocalField.instIsDiscreteValuationRingSubtypeMemSubringIntegerValueGroupWithZeroValuation, supp_eq_valuation_supp, ValueGroupWithZero.mk_eq_div, ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀, ValueGroupWithZero.leftInverse_embedding_orderMonoidIso, IsValuativeTopology.continuous_valuation, IsValuativeTopology.mem_nhds_iff', exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, ValuativeExtension.mapValueGroupWithZero_valuation, ValueGroupWithZero.embed_valuation_eq_restrict₀, IsValuativeTopology.mem_nhds_zero_iff, IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsNonarchimedeanLocalField.instCompactSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds_zero', IsValuativeTopology.hasBasis_nhds, IsValuativeTopology.hasBasis_nhds_zero, exists_valuation_div_valuation_eq, instCompatibleValueGroupWithZeroValuation, IsValuativeTopology.hasBasis_nhds', IsNonarchimedeanLocalField.isCompact_closedBall, valuation_surjective, ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq, IsValuativeTopology.v_eq_valuation, valuation_lt_symm_orderMonoidIso, ValueGroupWithZero.embedding_embed_valuation_eq, restrict_lt_orderMonoidIso, ValueGroupWithZero.lift_valuation, IsNonarchimedeanLocalField.instCompleteSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IsValuativeTopology.mem_nhds_iff, Valuation.exists_setOf_restrict_le_iff, ValueGroupWithZero.mk_eq_valuation
valueSetoid 📖CompOp
veq 📖MathDef
14 mathmath: zero_veq_iff, instSymmVeq, veq_trans, veq_refl, Valuation.veq_iff_eq, veq_comm, instReflVeq, veq.symm, veq_zero_iff, mul_veq_mul, veq.rfl, veq.refl, veq_rfl, veq_def
vle 📖MathDef
96 mathmath: pow_vle_pow_of_vle_one, pow_rel_pow_of_rel_one, ValueGroupWithZero.mk_eq_one, pow_rel_pow, valuation_eq_zero_iff, srel_iff, vge_of_veq, vle.rfl, rel_add, vle_mul_left_iff, vle.refl, ValueGroupWithZero.exact, rel_add_cases, vle_refl, vle_add_cases, mul_vle_mul_iff_left, zero_rel, pow_vle_pow, 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, pow_vle_pow_of_one_vle, mul_rel_mul_iff_left, Rel.trans, ValuativeExtension.vle_iff_vle, Valuation.vle_iff_le, mul_rel_mul, 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, vle_mul_right, zero_vle, vlt.not_vle, rel_trans, div_rel_one_iff, Valuation.vle_one_iff, rel_mul_right_iff, pow_rel_pow_of_one_rel, veq.vle, vle_div_iff, vle_trans, right_cancel_posSubmonoid, vle.trans', vle_mul_cancel, Valuation.rel_one_iff, rel_refl, rel_mul_left, 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, mul_vle_mul, vle_add, inv_vle_one, not_rel_one_zero, mul_vle_mul_right, ValueGroupWithZero.mk_le_mk, vle.trans, Valuation.Compatible.vle_iff_le, rel_mul_right, vlt.vle, vle_trans', rel_trans', mul_vle_mul_left, mul_rel_mul_iff_right, rel_mul_cancel, rel_div_iff, rel_mul, vle_of_veq, not_vle, Valuation.one_rel_iff, Rel.refl, veq_def, Rel.trans', vle_total
vlt 📖MathDef
66 mathmath: ValuativeExtension.srel_iff_srel, srel_iff, vlt.trans, inv_srel_one, zero_srel_coe_posSubmonoid, Valuation.Compatible.srel_iff_lt, ValueGroupWithZero.mk_pos, not_vgt_of_veq, mul_srel_mul, mul_srel_mul_of_srel_of_rel, mul_vlt_mul, zero_srel_mul, zero_srel_one, srel_mul_right_iff, vle.trans_vlt, not_vlt, not_vlt_zero, ValuativeExtension.vlt_iff_vlt, srel_mul_left, vlt_of_vle_of_vlt, zero_vlt_one, Valuation.srel_iff_lt, vle.not_vlt, ValueGroupWithZero.mk_lt_mk, Valuation.one_srel_iff, veq.not_vlt, srel_mul_right, zero_vlt_coe_posSubmonoid, vlt_mul_left_iff, srel_of_srel_of_rel, mul_vlt_mul_iff_right, Valuation.one_vlt_iff, one_vlt_inv, srel_mul_left_iff, mul_vlt_mul_left, SRel.trans, mul_srel_mul_iff_right, Valuation.srel_one_iff, not_vlt_of_veq, vlt_mul_right, SRel.trans_rel, vlt_of_vlt_of_vle, Valuation.vlt_one_iff, mul_srel_mul_of_rel_of_srel, not_srel_iff, Rel.trans_srel, posSubmonoid_def, vlt.trans_vle, pow_srel_pow, Valuation.vlt_iff_lt, zero_vlt_mul, mul_vlt_mul_right, inv_vlt_one, zero_srel_iff, vlt_mul_right_iff, one_srel_inv, veq.not_vgt, srel_of_rel_of_srel, mul_vlt_mul_of_vlt_of_vle, mul_srel_mul_iff_left, not_vle, pow_vlt_pow, vlt_mul_left, zero_vlt_iff, mul_vlt_mul_of_vle_of_vlt, mul_vlt_mul_iff_left
«term_<ᵥ_» 📖CompOp
«term_=ᵥ_» 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
div_rel_iff 📖mathematicalvle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
div_vle_iff
div_rel_one_iff 📖mathematicalvle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
div_vle_one_iff
div_vle_iff 📖mathematicalvle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_iff_left
div_mul_cancel₀
div_vle_one_iff 📖mathematicalvle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
div_vle_iff
one_mul
exists_valuation_div_valuation_eq 📖mathematicalSubmonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
ValueGroupWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
valuation
ValueGroupWithZero.ind
div_eq_mul_inv
Subtype.prop
Subtype.coe_eta
mul_one
one_mul
exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq 📖mathematicalSubmonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
posSubmonoid
ValueGroupWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
valuation
Units.val
MonoidWithZero.toMonoid
GroupWithZero.toMonoidWithZero
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 📖vle
ext_iff 📖mathematicalvleext
instCompatibleValueGroupWithZeroValuation 📖mathematicalValuation.Compatible
ValueGroupWithZero
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
valuation
mul_one
instIsNontrivialOfIsNontrivialOfCompatible 📖mathematicalValuation.IsNontrivial
CommRing.toRing
isNontrivial_iff_isNontrivial
instIsOrderedMonoidValueGroupWithZero 📖mathematicalIsOrderedMonoid
ValueGroupWithZero
CommMonoidWithZero.toCommMonoid
instCommMonoidWithZeroValueGroupWithZero
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
ValueGroupWithZero.ind
mul_mul_mul_comm
mul_vle_mul_left
instIsPrimeSupp 📖mathematicalIdeal.IsPrime
CommSemiring.toSemiring
CommRing.toCommSemiring
supp
supp_eq_valuation_supp
Valuation.instIsPrimeSuppOfNontrivialOfNoZeroDivisors
GroupWithZero.toNontrivial
GroupWithZero.noZeroDivisors
instMulArchimedeanValueGroupWithZeroOfIsRankLeOne 📖mathematicalMulArchimedean
ValueGroupWithZero
CommMonoidWithZero.toCommMonoid
instCommMonoidWithZeroValueGroupWithZero
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
IsRankLeOne.nonempty
MulArchimedean.comap
instReflVeq 📖mathematicalveqveq_rfl
instReflVle 📖mathematicalvlevle_rfl
instSymmVeq 📖mathematicalveqveq.symm
instValuativePreorderWithPreorder 📖mathematicalValuativePreorder
WithPreorder
instCommRingWithPreorder
instWithPreorder
instPreorderWithPreorder
inv_rel_one 📖mathematicalvle
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
inv_vle_one
inv_srel_one 📖mathematicalvlt
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
inv_vlt_one
inv_vle_one 📖mathematicalvle
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
one_div
div_vle_one_iff
inv_vlt_one 📖mathematicalvlt
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
Iff.not
one_vle_inv
isEquiv 📖mathematicalValuation.IsEquiv
CommRing.toRing
isNontrivial_iff_isNontrivial 📖mathematicalIsNontrivial
Valuation.IsNontrivial
CommRing.toRing
ValueGroupWithZero.ind
Valuation.Compatible.vle_iff_le
map_zero
MonoidWithZeroHomClass.toZeroHomClass
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
instReflLe
Iff.ne
Valuation.IsEquiv.eq_zero
isEquiv
instCompatibleValueGroupWithZeroValuation
Valuation.IsEquiv.eq_one_iff_eq_one
isNontrivial_iff_nontrivial_units 📖mathematicalIsNontrivial
Nontrivial
Units
ValueGroupWithZero
MonoidWithZero.toMonoid
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
eq_or_ne
GroupWithZero.toNontrivial
le_uniformizer_iff 📖mathematicalValueGroupWithZero
instLEValueGroupWithZero
uniformizer
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
instOneValueGroupWithZero
LE.le.trans_lt
uniformizer_lt_one
IsDiscrete.has_maximal_element
left_cancel_posSubmonoid 📖mathematicalvle
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
mul_rel_mul 📖mathematicalvlevle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul
mul_rel_mul_iff_left 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_iff_left
mul_rel_mul_iff_right 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_iff_right
mul_srel_mul 📖mathematicalvltvlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul
mul_srel_mul_iff_left 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_left
mul_srel_mul_iff_right 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_right
mul_srel_mul_of_rel_of_srel 📖mathematicalvle
vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_of_vle_of_vlt
mul_srel_mul_of_srel_of_rel 📖mathematicalvlt
vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_of_vlt_of_vle
mul_veq_mul 📖mathematicalveqveq
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul
veq.vle
veq.vge
mul_vle_mul 📖mathematicalvlevle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle.trans
mul_vle_mul_left
mul_vle_mul_right
mul_vle_mul_iff_left 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_mul_cancel
mul_vle_mul_left
mul_vle_mul_iff_right 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_comm
mul_vle_mul_left 📖mathematicalvlevle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_right 📖mathematicalvlevle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_comm
mul_vle_mul_left
mul_vlt_mul 📖mathematicalvltvlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle.trans_vlt
mul_vle_mul_right
vlt.vle
mul_vlt_mul_left
zero_vle
mul_vlt_mul_iff_left 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Iff.not
mul_vle_mul_iff_left
mul_vlt_mul_iff_right 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Iff.not
mul_vle_mul_iff_right
mul_vlt_mul_left 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_left
mul_vlt_mul_of_vle_of_vlt 📖mathematicalvle
vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt.trans_vle
mul_vlt_mul_right
mul_vle_mul_left
mul_vlt_mul_of_vlt_of_vle 📖mathematicalvlt
vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle.trans_vlt
mul_vle_mul_right
mul_vlt_mul_left
mul_vlt_mul_right 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_right
not_rel_one_zero 📖mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
not_vle_one_zero
not_srel_iff 📖mathematicalvlt
vle
not_vlt
not_vgt_of_veq 📖mathematicalveqvltvle.not_vlt
veq.vle
not_vle 📖mathematicalvle
vlt
not_vle_one_zero 📖mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
not_vlt 📖mathematicalvlt
vle
Iff.not_left
not_vle
not_vlt_of_veq 📖mathematicalveqvltvle.not_vlt
veq.vge
not_vlt_zero 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
one_apply_posSubmonoid 📖mathematicalDFunLike.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
Valuation.one_apply_of_ne_zero
one_rel_div_iff 📖mathematicalvle
Field.toCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
one_vle_div_iff
one_rel_inv 📖mathematicalvle
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
one_vle_inv
one_srel_inv 📖mathematicalvlt
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
one_vlt_inv
one_vle_div_iff 📖mathematicalvle
Field.toCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
vle_div_iff
one_mul
one_vle_inv 📖mathematicalvle
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
one_div
one_vle_div_iff
one_vlt_inv 📖mathematicalvlt
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
Iff.not
inv_vle_one
posSubmonoid_def 📖mathematicalSubmonoid
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
pow_rel_pow 📖mathematicalvlevle
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
pow_vle_pow
pow_rel_pow_of_one_rel 📖mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
vle
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
pow_vle_pow_of_one_vle
pow_rel_pow_of_rel_one 📖mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
vle
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
pow_vle_pow_of_vle_one
pow_srel_pow 📖mathematicalvltvlt
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
pow_vlt_pow
pow_vle_pow 📖mathematicalvlevle
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
pow_zero
pow_succ
mul_vle_mul
pow_vle_pow_of_one_vle 📖mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
vle
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
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 📖mathematicalvle
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
vle
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
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 📖mathematicalvltvlt
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
pow_one
pow_succ
rel_add 📖mathematicalvlevle
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_add
rel_add_cases 📖mathematicalvle
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_add_cases
rel_div_iff 📖mathematicalvle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_div_iff
rel_mul 📖mathematicalvlevle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul
rel_mul_cancel 📖mathematicalvle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
vlevle_mul_cancel
rel_mul_left 📖mathematicalvlevle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_right
rel_mul_left_iff 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_iff_right
rel_mul_right 📖mathematicalvlevle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_left
rel_mul_right_iff 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_mul_right_iff
rel_refl 📖mathematicalvlevle_refl
rel_rfl 📖mathematicalvlevle_rfl
rel_total 📖mathematicalvlevle_total
rel_trans 📖mathematicalvlevlevle_trans
rel_trans' 📖mathematicalvlevlevle_trans'
rel_zero_iff 📖mathematicalvle
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_zero_iff
restrict_lt_orderMonoidIso 📖mathematicalMonoidWithZeroHom.ValueGroup₀
MonoidWithZeroHom
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
Ring.toSemiring
CommRing.toRing
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
MonoidWithZeroHom.funLike
MonoidWithZeroHomClass.toMonoidWithZeroHom
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
Valuation.instFunLike
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
Semiring.toMonoidWithZero
MonoidWithZeroHom.monoidWithZeroHomClass
Preorder.toLT
WithZero.instPreorder
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Subtype.preorder
Units.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
MonoidWithZeroHom.ValueGroup₀.instLinearOrderedCommGroupWithZero
Valuation.restrict
OrderMonoidIso
ValueGroupWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
instLinearOrderValueGroupWithZero
instMulValueGroupWithZero
MulZeroClass.toMul
WithZero.instMulZeroClass
Subgroup.mul
EquivLike.toFunLike
OrderMonoidIso.instEquivLike
ValueGroupWithZero.orderMonoidIso
instLinearOrderedCommGroupWithZeroValueGroupWithZero
valuation
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
MonoidWithZeroHom.monoidWithZeroHomClass
OrderMonoidIso.symm_apply_apply
valuation_lt_symm_orderMonoidIso
right_cancel_posSubmonoid 📖mathematicalvle
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
srel_iff 📖mathematicalvlt
vle
srel_mul_left 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_right
srel_mul_left_iff 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_right
srel_mul_right 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_right
srel_mul_right_iff 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_left
srel_of_rel_of_srel 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_left
srel_of_srel_of_rel 📖mathematicalvlt
vle
vltvlt_of_vlt_of_vle
supp_def 📖mathematicalIdeal
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
supp_eq_valuation_supp 📖mathematicalsupp
Valuation.supp
ValueGroupWithZero
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
valuation
Ideal.ext
valuation_eq_zero_iff
uniformizer_inv_le_iff 📖mathematicalValueGroupWithZero
instLEValueGroupWithZero
instInvValueGroupWithZero
uniformizer
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
instOneValueGroupWithZero
bot_lt_iff_ne_bot
inv_le_comm₀
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
MulPosReflectLE.toMulPosReflectLT
MulPosStrictMono.toMulPosReflectLE
LinearOrderedCommMonoidWithZero.toMulPosStrictMono
uniformizer_pos
le_uniformizer_iff
inv_lt_one₀
uniformizer_lt_one 📖mathematicalValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
uniformizer
instOneValueGroupWithZero
IsDiscrete.has_maximal_element
uniformizer_ne_zero 📖LT.lt.ne'
uniformizer_pos
uniformizer_pos 📖mathematicalValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
instZeroValueGroupWithZero
uniformizer
IsNontrivial.exists_lt_one
LT.lt.trans_le
le_uniformizer_iff
val_posSubmonoid_ne_zero 📖Subtype.prop
Mathlib.Tactic.Contrapose.contrapose₃
posSubmonoid_def
valuation_eq_zero_iff 📖mathematicalDFunLike.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
ValueGroupWithZero.mk_eq_zero
valuation_lt_symm_orderMonoidIso 📖mathematicalValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderValueGroupWithZero
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
valuation
OrderMonoidIso
MonoidWithZeroHom.ValueGroup₀
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
WithZero.instPreorder
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Subtype.preorder
Units.instPreorder
LinearOrderedCommMonoidWithZero.toLinearOrder
MulZeroClass.toMul
WithZero.instMulZeroClass
Subgroup.mul
instMulValueGroupWithZero
EquivLike.toFunLike
OrderMonoidIso.instEquivLike
OrderMonoidIso.symm
ValueGroupWithZero.orderMonoidIso
MonoidWithZeroHom
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
Ring.toSemiring
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
MonoidWithZeroHomClass.toMonoidWithZeroHom
MonoidWithZeroHom.monoidWithZeroHomClass
MonoidWithZeroHom.ValueGroup₀.instLinearOrderedCommGroupWithZero
Valuation.restrict
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
MonoidWithZeroHom.monoidWithZeroHomClass
map_lt_map_iff
OrderMonoidIso.instOrderIsoClass
ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀
OrderMonoidIso.apply_symm_apply
valuation_posSubmonoid_ne_zero 📖valuation_eq_zero_iff
Subtype.prop
valuation_surjective 📖mathematicalValueGroupWithZero
Field.toCommRing
DFunLike.coe
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
valuation
ValueGroupWithZero.ind
ValueGroupWithZero.mk_eq_valuation
veq_comm 📖mathematicalveqantisymmRel_comm
veq_def 📖mathematicalveq
vle
veq_refl 📖mathematicalveqAntisymmRel.rfl
instReflVle
veq_rfl 📖mathematicalveqveq_refl
veq_trans 📖mathematicalveqveqAntisymmRel.trans
instIsTransOfTrans
veq_zero_iff 📖mathematicalveq
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
veq_comm
zero_veq_iff
vge_of_veq 📖mathematicalveqvle
vle_add 📖mathematicalvlevle
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_add_cases 📖mathematicalvle
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_add
vle.rfl
vle_total
vle_div_iff 📖mathematicalvle
Field.toCommRing
DivInvMonoid.toDiv
DivisionRing.toDivInvMonoid
Field.toDivisionRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_iff_left
div_mul_cancel₀
vle_mul_cancel 📖mathematicalvle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
vle
vle_mul_left_iff 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_iff_right
vle_mul_right 📖mathematicalvlevle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_left
vle_mul_right_iff 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vle_mul_iff_left
vle_of_veq 📖mathematicalveqvle
vle_refl 📖mathematicalvlevle_total
vle_rfl 📖mathematicalvlevle_refl
vle_total 📖mathematicalvle
vle_trans 📖mathematicalvlevle
vle_trans' 📖mathematicalvlevlevle.trans
vle_zero_iff 📖mathematicalvle
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
supp_def
Ideal.eq_bot_of_prime
instIsPrimeSupp
Ideal.mem_bot
vlt_mul_left 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_right
vlt_mul_left_iff 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_right
vlt_mul_right 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_left
vlt_mul_right_iff 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_vlt_mul_iff_left
vlt_of_vle_of_vlt 📖mathematicalvle
vlt
vltlt_of_le_of_lt
vlt_of_vlt_of_vle 📖mathematicalvlt
vle
vltlt_of_lt_of_le
zero_rel 📖mathematicalvle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
zero_vle
zero_srel_coe_posSubmonoid 📖mathematicalvlt
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
zero_vlt_coe_posSubmonoid
zero_srel_iff 📖mathematicalvlt
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
zero_vlt_iff
zero_srel_mul 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
zero_vlt_mul
zero_srel_one 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
zero_vlt_one
zero_veq_iff 📖mathematicalveq
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vle_zero_iff
zero_vle 📖mathematicalvle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
MulZeroClass.zero_mul
one_mul
mul_vle_mul_left
vle_total
not_vle_one_zero
zero_vlt_coe_posSubmonoid 📖mathematicalvlt
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
Subtype.prop
zero_vlt_iff 📖mathematicalvlt
Field.toCommRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
zero_vlt_mul 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Mathlib.Tactic.Contrapose.contrapose₁
not_vlt
vle_mul_cancel
mul_comm
MulZeroClass.mul_zero
zero_vlt_one 📖mathematicalvlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
not_vle_one_zero

ValuativeRel.IsDiscrete

Theorems

NameKindAssumesProvesValidatesDepends On
has_maximal_element 📖mathematicalValuativeRel.ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
ValuativeRel.instLEValueGroupWithZero

ValuativeRel.IsNontrivial

Theorems

NameKindAssumesProvesValidatesDepends On
condition 📖mathematicalValuativeRel.ValueGroupWithZero
exists_lt_one 📖mathematicalValuativeRel.ValueGroupWithZero
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
condition
lt_or_lt_iff_ne
zero_lt_iff
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
LinearOrderedCommMonoidWithZero.toZeroLeOneClass

ValuativeRel.IsRankLeOne

Theorems

NameKindAssumesProvesValidatesDepends On
nonempty 📖mathematicalValuativeRel.RankLeOneStruct
of_valuativeExtension 📖mathematicalValuativeRel.IsRankLeOnenonempty
StrictMono.comp
ValuativeExtension.mapValueGroupWithZero_strictMono

ValuativeRel.RankLeOneStruct

Definitions

NameCategoryTheorems
emb 📖CompOp
1 mathmath: strictMono

Theorems

NameKindAssumesProvesValidatesDepends On
strictMono 📖mathematicalStrictMono
ValuativeRel.ValueGroupWithZero
NNReal
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
NNReal.instPartialOrder
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
NNReal.instSemiring
MonoidWithZeroHom.funLike
emb

ValuativeRel.Rel

Theorems

NameKindAssumesProvesValidatesDepends On
refl 📖mathematicalValuativeRel.vleValuativeRel.vle.refl
rfl 📖mathematicalValuativeRel.vleValuativeRel.vle.rfl
trans 📖mathematicalValuativeRel.vleValuativeRel.vleValuativeRel.vle.trans
trans' 📖mathematicalValuativeRel.vleValuativeRel.vleValuativeRel.vle.trans'
trans_srel 📖mathematicalValuativeRel.vlt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
ValuativeRel.vlt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
ValuativeRel.srel_of_rel_of_srel

ValuativeRel.SRel

Theorems

NameKindAssumesProvesValidatesDepends On
rel 📖mathematicalValuativeRel.vltValuativeRel.vleValuativeRel.vlt.vle
trans 📖mathematicalValuativeRel.vltValuativeRel.vltValuativeRel.vlt.trans
trans_rel 📖mathematicalValuativeRel.vlt
ValuativeRel.vle
ValuativeRel.vltValuativeRel.vlt.trans_vle

ValuativeRel.ValueGroupWithZero

Definitions

NameCategoryTheorems
embed 📖CompOp
5 mathmath: embed_strictMono, embed_valuation_eq_restrict₀, orderMonoidIso_embed, embed_mk, embedding_embed_valuation_eq
lift₂ 📖CompOp
1 mathmath: lift₂_mk
mk 📖CompOp
orderMonoidIso 📖CompOp
7 mathmath: orderMonoidIso_valuation_eq_restrict₀, leftInverse_embedding_orderMonoidIso, orderMonoidIso_mk, embedding_orderMonoidIso_valuation_eq, ValuativeRel.valuation_lt_symm_orderMonoidIso, ValuativeRel.restrict_lt_orderMonoidIso, orderMonoidIso_strictMono
valueGroupWithZero_equiv_valueGroup₀ 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
bot_eq_zero 📖mathematicalBot.bot
ValuativeRel.ValueGroupWithZero
ValuativeRel.instBotValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
embed_mk 📖mathematicalDFunLike.coe
MonoidWithZeroHom
ValuativeRel.ValueGroupWithZero
MonoidWithZeroHom.ValueGroup₀
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
MonoidWithZero.toMulZeroOneClass
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
WithZero.instMulZeroOneClass
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZeroHom.funLike
embed
WithZero.div
Subgroup.div
MonoidWithZeroHom.ValueGroup₀.restrict₀
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
Submonoid.instSetLike
ValuativeRel.posSubmonoid
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
embed_strictMono 📖mathematicalStrictMono
ValuativeRel.ValueGroupWithZero
MonoidWithZeroHom.ValueGroup₀
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
WithZero.instPreorder
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Subtype.preorder
Units.instPreorder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
WithZero.instMulZeroOneClass
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZeroHom.funLike
embed
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
ValuativeRel.exists_valuation_div_valuation_eq
MonoidWithZeroHom.monoidWithZeroHomClass
StrictMono.lt_iff_lt
MonoidWithZeroHom.ValueGroup₀.embedding_strictMono
map_div₀
div_lt_div_iff₀
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
lift.congr_simp
GroupWithZero.toNontrivial
div_one
MonoidWithZeroHom.ValueGroup₀.embedding_restrict₀
map_mul
MonoidHomClass.toMulHomClass
Valuation.IsEquiv.lt_iff_lt
ValuativeRel.isEquiv
ValuativeRel.instCompatibleValueGroupWithZeroValuation
embed_valuation_eq_restrict₀ 📖mathematicalDFunLike.coe
MonoidWithZeroHom
ValuativeRel.ValueGroupWithZero
MonoidWithZeroHom.ValueGroup₀
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
MonoidWithZero.toMulZeroOneClass
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
WithZero.instMulZeroOneClass
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZeroHom.funLike
embed
ValuativeRel.valuation
MonoidWithZeroHom.ValueGroup₀.restrict₀
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
MonoidWithZeroHom.monoidWithZeroHomClass
div_one
embedding_embed_valuation_eq 📖mathematicalDFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.ValueGroup₀
ValuativeRel.ValueGroupWithZero
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
ValuativeRel.valuation
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
WithZero.instMulZeroOneClass
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
MonoidWithZeroHom.ValueGroup₀.embedding
embed
ValuativeRel.instCompatibleValueGroupWithZeroValuation
ind
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
ValuativeRel.instCompatibleValueGroupWithZeroValuation
mk_eq_div
map_div₀
MonoidWithZeroHom.monoidWithZeroHomClass
embed_valuation_eq_restrict₀
MonoidWithZeroHom.ValueGroup₀.embedding_restrict₀
embedding_orderMonoidIso_valuation_eq 📖mathematicalDFunLike.coe
MonoidWithZeroHom
MonoidWithZeroHom.ValueGroup₀
ValuativeRel.ValueGroupWithZero
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
ValuativeRel.valuation
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
WithZero.instMulZeroOneClass
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
MonoidWithZeroHom.ValueGroup₀.embedding
OrderMonoidIso
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
WithZero.instPreorder
Subtype.preorder
Units.instPreorder
LinearOrderedCommMonoidWithZero.toLinearOrder
ValuativeRel.instMulValueGroupWithZero
MulZeroClass.toMul
WithZero.instMulZeroClass
Subgroup.mul
EquivLike.toFunLike
OrderMonoidIso.instEquivLike
orderMonoidIso
ValuativeRel.instCompatibleValueGroupWithZeroValuation
embedding_embed_valuation_eq
exact 📖mathematicalValuativeRel.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
ind 📖
inv_mk 📖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
leftInverse_embedding_orderMonoidIso 📖mathematicalValuativeRel.ValueGroupWithZero
MonoidWithZeroHom.ValueGroup₀
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
CommRing.toRing
Valuation.instFunLike
ValuativeRel.valuation
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
DFunLike.coe
MonoidWithZeroHom
WithZero.instMulZeroOneClass
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZero.toMulZeroOneClass
MonoidWithZeroHom.funLike
MonoidWithZeroHom.ValueGroup₀.embedding
OrderMonoidIso
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
WithZero.instPreorder
Subtype.preorder
Units.instPreorder
LinearOrderedCommMonoidWithZero.toLinearOrder
ValuativeRel.instMulValueGroupWithZero
MulZeroClass.toMul
WithZero.instMulZeroClass
Subgroup.mul
EquivLike.toFunLike
OrderMonoidIso.instEquivLike
orderMonoidIso
ValuativeRel.instCompatibleValueGroupWithZeroValuation
embedding_orderMonoidIso_valuation_eq
lift_mk 📖mathematicallift
lift_mul 📖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
ind
lift_one 📖mathematicallift
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
lift_valuation 📖mathematicallift
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
lift_zero 📖mathematicallift
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
lift₂_mk 📖mathematicallift₂
mk_eq_div 📖mathematicalValuativeRel.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
eq_div_iff
ValuativeRel.valuation_posSubmonoid_ne_zero
mul_one
mk_eq_mk 📖mathematicalValuativeRel.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
Quotient.eq
mk_eq_one 📖mathematicalValuativeRel.ValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
ValuativeRel.vle
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
mul_one
one_mul
mk_eq_valuation 📖mathematicalField.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
Valuation.map_div
mk_eq_div
mk_eq_zero 📖mathematicalValuativeRel.ValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
ValuativeRel.vle
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
mul_one
MulZeroClass.zero_mul
sound
mk_le_mk 📖mathematicalValuativeRel.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
mk_lt_mk 📖mathematicalValuativeRel.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
lt_iff_not_ge
ValuativeRel.not_vle
mk_mul_mk 📖mathematicalValuativeRel.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
mk_one_one 📖mathematicalAddMonoidWithOne.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
sound
mul_one
mk_pos 📖mathematicalValuativeRel.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
mk_zero
MulZeroClass.zero_mul
mul_one
mk_self 📖mathematicalSubmonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
SetLike.instMembership
Submonoid.instSetLike
ValuativeRel.posSubmonoid
ValuativeRel.ValueGroupWithZero
ValuativeRel.instOneValueGroupWithZero
sound
mul_one
one_mul
mk_zero 📖mathematicalMulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
ValuativeRel.ValueGroupWithZero
ValuativeRel.instZeroValueGroupWithZero
mk_eq_zero
ValuativeRel.vle.rfl
orderMonoidIso_embed 📖mathematicalValuation.IsEquiv
CommRing.toRing
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
DFunLike.coe
OrderMonoidIso
MonoidWithZeroHom.ValueGroup₀
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Semiring.toMonoidWithZero
Ring.toSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
WithZero.instPreorder
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Subtype.preorder
Units.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrderedCommMonoidWithZero.toLinearOrder
MulZeroClass.toMul
WithZero.instMulZeroClass
Subgroup.mul
EquivLike.toFunLike
OrderMonoidIso.instEquivLike
Valuation.IsEquiv.orderMonoidIso
MonoidWithZeroHom
ValuativeRel.ValueGroupWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
MonoidWithZero.toMulZeroOneClass
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
WithZero.instMulZeroOneClass
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZeroHom.funLike
embed
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
ind
MonoidWithZeroHom.monoidWithZeroHomClass
map_div₀
MulEquivClass.toMonoidWithZeroHomClass
OrderMonoidIso.instMulEquivClass
Valuation.IsEquiv.orderMonoidIso_spec
orderMonoidIso_mk 📖mathematicalDFunLike.coe
OrderMonoidIso
ValuativeRel.ValueGroupWithZero
MonoidWithZeroHom.ValueGroup₀
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
WithZero.instPreorder
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Subtype.preorder
Units.instPreorder
LinearOrderedCommMonoidWithZero.toLinearOrder
ValuativeRel.instMulValueGroupWithZero
MulZeroClass.toMul
WithZero.instMulZeroClass
Subgroup.mul
EquivLike.toFunLike
OrderMonoidIso.instEquivLike
orderMonoidIso
WithZero.div
Subgroup.div
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
WithZero.instMulZeroOneClass
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZeroHom.funLike
MonoidWithZeroHom.ValueGroup₀.restrict₀
Submonoid
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
Submonoid.instSetLike
ValuativeRel.posSubmonoid
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
orderMonoidIso_strictMono 📖mathematicalStrictMono
ValuativeRel.ValueGroupWithZero
MonoidWithZeroHom.ValueGroup₀
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
WithZero.instPreorder
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Subtype.preorder
Units.instPreorder
LinearOrderedCommMonoidWithZero.toLinearOrder
DFunLike.coe
OrderMonoidIso
ValuativeRel.instMulValueGroupWithZero
MulZeroClass.toMul
WithZero.instMulZeroClass
Subgroup.mul
EquivLike.toFunLike
OrderMonoidIso.instEquivLike
orderMonoidIso
embed_strictMono
orderMonoidIso_valuation_eq_restrict₀ 📖mathematicalDFunLike.coe
OrderMonoidIso
ValuativeRel.ValueGroupWithZero
MonoidWithZeroHom.ValueGroup₀
Valuation
LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero
CommRing.toRing
Valuation.instFunLike
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
LinearOrderedCommGroupWithZero.toCommGroupWithZero
ValuationClass.toMonoidWithZeroHomClass
Valuation.instValuationClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ValuativeRel.instLinearOrderValueGroupWithZero
WithZero.instPreorder
Units
MonoidWithZero.toMonoid
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
MonoidWithZeroHom.valueGroup
Subtype.preorder
Units.instPreorder
LinearOrderedCommMonoidWithZero.toLinearOrder
ValuativeRel.instMulValueGroupWithZero
MulZeroClass.toMul
WithZero.instMulZeroClass
Subgroup.mul
EquivLike.toFunLike
OrderMonoidIso.instEquivLike
orderMonoidIso
ValuativeRel.instLinearOrderedCommGroupWithZeroValueGroupWithZero
ValuativeRel.valuation
MonoidWithZeroHom
MonoidWithZero.toMulZeroOneClass
WithZero.instMulZeroOneClass
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Subgroup.toGroup
MonoidWithZeroHom.funLike
MonoidWithZeroHom.ValueGroup₀.restrict₀
embed_valuation_eq_restrict₀
sound 📖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

ValuativeRel.veq

Theorems

NameKindAssumesProvesValidatesDepends On
not_vgt 📖mathematicalValuativeRel.veqValuativeRel.vltValuativeRel.not_vgt_of_veq
not_vlt 📖mathematicalValuativeRel.veqValuativeRel.vltValuativeRel.not_vlt_of_veq
refl 📖mathematicalValuativeRel.veqValuativeRel.veq_refl
rfl 📖mathematicalValuativeRel.veqValuativeRel.veq_rfl
vge 📖mathematicalValuativeRel.veqValuativeRel.vleValuativeRel.vge_of_veq
vle 📖mathematicalValuativeRel.veqValuativeRel.vleValuativeRel.vle_of_veq

ValuativeRel.vle

Theorems

NameKindAssumesProvesValidatesDepends On
not_vlt 📖mathematicalValuativeRel.vleValuativeRel.vltValuativeRel.not_vlt
refl 📖mathematicalValuativeRel.vleValuativeRel.vle_refl
rfl 📖mathematicalValuativeRel.vleValuativeRel.vle_rfl
trans 📖mathematicalValuativeRel.vleValuativeRel.vleValuativeRel.vle_trans
trans' 📖mathematicalValuativeRel.vleValuativeRel.vleValuativeRel.vle_trans'
trans_vlt 📖mathematicalValuativeRel.vle
ValuativeRel.vlt
ValuativeRel.vltValuativeRel.vlt_of_vle_of_vlt

ValuativeRel.vlt

Theorems

NameKindAssumesProvesValidatesDepends On
ne_zero 📖ValuativeRel.vltValuativeRel.not_vlt_zero
not_vle 📖mathematicalValuativeRel.vltValuativeRel.vleValuativeRel.not_vle
trans 📖mathematicalValuativeRel.vltValuativeRel.vlttrans_vle
vle
trans_vle 📖mathematicalValuativeRel.vlt
ValuativeRel.vle
ValuativeRel.vltValuativeRel.vlt_of_vlt_of_vle
vle 📖mathematicalValuativeRel.vltValuativeRel.vlele_of_lt

(root)

Definitions

NameCategoryTheorems
ValuativeExtension 📖CompData
ValuativePreorder 📖CompData
1 mathmath: ValuativeRel.instValuativePreorderWithPreorder
«term_≤ᵥ_» 📖CompOp

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