Documentation Verification Report

Class

πŸ“ Source: Mathlib/Algebra/Order/Archimedean/Class.lean

Statistics

MetricCount
DefinitionsArchimedeanClass, addSubgroup, ballAddSubgroup, closedBallAddSubgroup, instInhabited, instLinearOrder, instOrderTop, liftOrderHom, liftβ‚‚, mk, orderHom, out, subsemigroup, ArchimedeanOrder, instInhabited, instLE, instLT, instPreorder, of, orderHom, val, FiniteArchimedeanClass, addSubgroup, ballAddSubgroup, closedBallAddSubgroup, congrOrderIso, liftOrderHom, mk, toUpperSetAddArchimedeanClass, withTopOrderIso, FiniteMulArchimedeanClass, ballSubgroup, closedBallSubgroup, congrOrderIso, liftOrderHom, mk, subgroup, toUpperSetMulArchimedeanClass, withTopOrderIso, MulArchimedeanClass, ballSubgroup, closedBallSubgroup, instInhabited, instLinearOrder, instOrderTop, liftOrderHom, liftβ‚‚, mk, orderHom, out, subgroup, subsemigroup, MulArchimedeanOrder, instInhabited, instLE, instLT, instPreorder, of, orderHom, val
60
TheoremsaddSubgroup_antitone, addSubgroup_eq_bot, addSubgroup_strictAntiOn, archimedean_of_mk_eq_mk, ballAddSubgroup_antitone, ballAddSubgroup_top, closedBallAddSubgroup_top, forall, ind, instNontrivial, instSubsingleton, liftOrderHom_mk, lift_mk, liftβ‚‚_mk, lt_of_mk_lt_mk_of_nonneg, lt_of_mk_lt_mk_of_nonpos, map_mk_eq, map_mk_le, mem_addSubgroup_iff, mem_ballAddSubgroup_iff, mem_closedBallAddSubgroup_iff, min_le_mk_add, min_le_mk_of_le_of_le, min_le_mk_sub, mk_abs, mk_add_eq_mk_left, mk_add_eq_mk_right, mk_add_lt_mk_left_iff, mk_add_lt_mk_right_iff, mk_antitoneOn, mk_eq_mk, mk_eq_mk_of_archimedean, mk_eq_top_iff, mk_le_mk, mk_le_mk_iff_lt, mk_le_mk_of_abs, mk_left_le_mk_add, mk_left_le_mk_add_iff, mk_left_le_mk_sub, mk_left_le_mk_sub_iff, mk_lt_mk, mk_monotoneOn, mk_neg, mk_out, mk_right_le_mk_add, mk_right_le_mk_add_iff, mk_right_le_mk_sub, mk_right_le_mk_sub_iff, mk_sub_comm, mk_sub_eq_mk_left, mk_sub_eq_mk_right, mk_sub_lt_mk_left_iff, mk_sub_lt_mk_right_iff, mk_sum, mk_surjective, mk_zero, orderHom_injective, orderHom_mk, orderHom_top, out_top, pos_of_pos_of_mk_lt, range_mk, subsemigroup_eq_addSubgroup_of_ne_top, subsemigroup_strictAnti, top_eq_mk_iff, instNonempty, instSubsingleton, instTotalLe, le_def, lt_def, of_symm_eq, of_val, val_of, val_symm_eq, addSubgroup_eq_bot, addSubgroup_strictAnti, ballAddSubgroup_strictAnti, coe_congrOrderIso_apply, congrOrderIso_symm, ind, instNonemptyOfNontrivial, instSubsingletonOfAddArchimedean, liftOrderHom_mk, lift_mk, mem_addSubgroup_iff, mem_ballAddSubgroup_iff, mem_closedBallAddSubgroup_iff, min_le_mk_add, mk_le_mk, mk_lt_mk, mk_neg, subsemigroup_eq_addSubgroup, val_mk, withTopOrderIso_apply_coe, withTopOrderIso_symm_apply, ballSubgroup_strictAnti, coe_congrOrderIso_apply, congrOrderIso_symm, ind, instNonemptyOfNontrivial, instSubsingletonOfMulArchimedean, liftOrderHom_mk, lift_mk, mem_ballSubgroup_iff, mem_closedBallSubgroup_iff, mem_subgroup_iff, min_le_mk_mul, mk_inv, mk_le_mk, mk_lt_mk, subgroup_eq_bot, subgroup_strictAnti, subsemigroup_eq_subgroup, val_mk, withTopOrderIso_apply_coe, withTopOrderIso_symm_apply, ballSubgroup_antitone, ballSubgroup_top, closedBallSubgroup_top, forall, ind, instNontrivial, instSubsingleton, liftOrderHom_mk, lift_mk, liftβ‚‚_mk, lt_of_mk_lt_mk_of_le_one, lt_of_mk_lt_mk_of_one_le, map_mk_eq, map_mk_le, mem_ballSubgroup_iff, mem_closedBallSubgroup_iff, mem_subgroup_iff, min_le_mk_div, min_le_mk_mul, min_le_mk_of_le_of_le, mk_antitoneOn, mk_div_comm, mk_div_eq_mk_left, mk_div_eq_mk_right, mk_div_lt_mk_left_iff, mk_div_lt_mk_right_iff, mk_eq_mk, mk_eq_mk_of_mulArchimedean, mk_eq_top_iff, mk_inv, mk_le_mk, mk_le_mk_iff_lt, mk_le_mk_of_mabs, mk_left_le_mk_div, mk_left_le_mk_div_iff, mk_left_le_mk_mul, mk_left_le_mk_mul_iff, mk_lt_mk, mk_mabs, mk_monotoneOn, mk_mul_eq_mk_left, mk_mul_eq_mk_right, mk_mul_lt_mk_left_iff, mk_mul_lt_mk_right_iff, mk_one, mk_out, mk_prod, mk_right_le_mk_div, mk_right_le_mk_div_iff, mk_right_le_mk_mul, mk_right_le_mk_mul_iff, mk_surjective, mulArchimedean_of_mk_eq_mk, one_lt_of_one_lt_of_mk_lt, orderHom_injective, orderHom_mk, orderHom_top, out_top, range_mk, subgroup_antitone, subgroup_eq_bot, subgroup_strictAntiOn, subsemigroup_eq_subgroup_of_ne_top, subsemigroup_strictAnti, top_eq_mk_iff, instNonempty, instSubsingleton, instTotalLe, le_def, lt_def, of_symm_eq, of_val, val_of, val_symm_eq
190
Total250

ArchimedeanClass

Definitions

NameCategoryTheorems
addSubgroup πŸ“–CompOp
5 mathmath: subsemigroup_eq_addSubgroup_of_ne_top, addSubgroup_antitone, mem_addSubgroup_iff, addSubgroup_eq_bot, addSubgroup_strictAntiOn
ballAddSubgroup πŸ“–CompOp
4 mathmath: ballAddSubgroup_top, ballAddSubgroup_antitone, toAddSubgroup_ball, mem_ballAddSubgroup_iff
closedBallAddSubgroup πŸ“–CompOp
3 mathmath: closedBallAddSubgroup_top, mem_closedBallAddSubgroup_iff, toAddSubgroup_closedBall
instInhabited πŸ“–CompOpβ€”
instLinearOrder πŸ“–CompOp
118 mathmath: HahnEmbedding.IsPartial.baseEmbedding_le, FiniteArchimedeanClass.mem_addSubgroup_iff, closedBallAddSubgroup_top, addSubgroup_antitone, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, min_le_mk_of_le_of_le, FiniteArchimedeanClass.mk_lt_mk, FiniteResidueField.mk_eq_zero, mk_le_mk, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, HahnEmbedding.Seed.baseEmbedding_strictMono, FiniteArchimedeanClass.val_mk, mk_add_lt_mk_left_iff, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, mk_left_le_mk_sub_iff, mk_le_mk_smul, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, HahnEmbedding.Partial.isWF_support_evalCoeff, HahnEmbedding.Partial.orderTop_eq_iff, top_eq_mk_iff, instIsOrderedAddMonoid, mk_lt_mk, FiniteElement.not_isUnit_iff_mk_pos, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, orderHom_zero, mem_ball_iff, mk_monotoneOn, mk_sub_lt_mk_right_iff, HahnEmbedding.IsPartial.strictMono, mk_add_lt_mk_right_iff, ballAddSubgroup_top, FiniteArchimedeanClass.liftOrderHom_mk, mk_map_nonneg_of_archimedean, HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratum, HahnEmbedding.IsPartial.truncLT_mem_range, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, mk_natCast_nonneg, mk_right_le_mk_sub_iff, mk_zero, Hyperreal.archimedeanClassMk_pos_of_tendsto, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, FiniteArchimedeanClass.mem_ball_iff, min_le_mk_add, mk_le_mk_iff_lt, HahnEmbedding.Partial.eval_smul, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, mem_addSubgroup_iff, addSubgroup_eq_bot, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, mk_le_mk_of_abs, mk_left_le_mk_add_iff, FiniteResidueField.mk_eq_mk, stdPart_monotoneOn, ballAddSubgroup_antitone, out_top, subsemigroup_strictAnti, ball_top, FiniteArchimedeanClass.mk_le_mk, HahnSeries.archimedeanClassOrderIsoWithTop_apply, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff_of_orderTop_ofLex, mk_le_mk_iff_ratCast, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, mk_le_mk_iff_denselyOrdered, hahnEmbedding_isOrderedModule_rat, FiniteArchimedeanClass.congrOrderIso_symm, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, FiniteArchimedeanClass.withTopOrderIso_symm_apply, HahnEmbedding.Partial.mem_domain, HahnEmbedding.Seed.mem_domain_baseEmbedding, mk_intCast_nonneg, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, DivisibleHull.archimedeanClassOrderIso_apply, Hyperreal.archimedeanClassMk_omega_neg, Hyperreal.archimedeanClassMk_coe_nonneg, mem_closedBall_iff, mk_ratCast_nonneg, Hyperreal.tendsto_atBot_iff, FiniteArchimedeanClass.addSubgroup_strictAnti, mk_le_mk_add_of_archimedean, mk_nonneg_of_le_of_le_of_archimedean, FiniteArchimedeanClass.coe_congrOrderIso_apply, mk_eq_top_iff, mk_le_add_mk_of_archimedean, mk_right_le_mk_add_iff, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, DivisibleHull.archimedeanClassOrderIso_symm_apply, addSubgroup_strictAntiOn, FiniteArchimedeanClass.submodule_strictAnti, mem_ballAddSubgroup_iff, min_le_mk_sub, eq_zero_or_top_of_archimedean, FiniteArchimedeanClass.ball_strictAnti, orderHom_top, HahnEmbedding.Partial.eval_zero, HahnSeries.finiteArchimedeanClassOrderIso_apply, FiniteArchimedeanClass.min_le_mk_add, liftOrderHom_mk, orderHom_mk, mk_antitoneOn, HahnEmbedding.Partial.exists_domain_eq_top, mk_sub_lt_mk_left_iff, FiniteArchimedeanClass.addSubgroup_eq_bot, HahnEmbedding.Partial.exists_isMax, ball_antitone, HahnEmbedding.Seed.domain_baseEmbedding, mem_closedBallAddSubgroup_iff, FiniteArchimedeanClass.withTopOrderIso_apply_coe, FiniteArchimedeanClass.mem_closedBall_iff, closedBall_top, hahnEmbedding_isOrderedAddMonoid, orderHom_injective, Hyperreal.archimedeanClassMk_epsilon_pos, Hyperreal.tendsto_atTop_iff, hahnEmbedding_isOrderedModule, HahnEmbedding.Partial.toOrderAddMonoidHom_injective
instOrderTop πŸ“–CompOp
57 mathmath: HahnEmbedding.IsPartial.baseEmbedding_le, FiniteArchimedeanClass.mem_addSubgroup_iff, closedBallAddSubgroup_top, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, FiniteArchimedeanClass.mk_lt_mk, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, HahnEmbedding.Seed.baseEmbedding_strictMono, FiniteArchimedeanClass.val_mk, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, HahnEmbedding.Partial.isWF_support_evalCoeff, HahnEmbedding.Partial.orderTop_eq_iff, top_eq_mk_iff, HahnEmbedding.IsPartial.strictMono, ballAddSubgroup_top, FiniteArchimedeanClass.liftOrderHom_mk, HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratum, HahnEmbedding.IsPartial.truncLT_mem_range, mk_zero, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, FiniteArchimedeanClass.mem_ball_iff, HahnEmbedding.Partial.eval_smul, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, out_top, ball_top, FiniteArchimedeanClass.mk_le_mk, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, hahnEmbedding_isOrderedModule_rat, FiniteArchimedeanClass.congrOrderIso_symm, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, FiniteArchimedeanClass.withTopOrderIso_symm_apply, HahnEmbedding.Partial.mem_domain, HahnEmbedding.Seed.mem_domain_baseEmbedding, FiniteArchimedeanClass.addSubgroup_strictAnti, FiniteArchimedeanClass.coe_congrOrderIso_apply, mk_eq_top_iff, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, FiniteArchimedeanClass.submodule_strictAnti, eq_zero_or_top_of_archimedean, FiniteArchimedeanClass.ball_strictAnti, orderHom_top, HahnEmbedding.Partial.eval_zero, HahnSeries.finiteArchimedeanClassOrderIso_apply, FiniteArchimedeanClass.min_le_mk_add, HahnEmbedding.Partial.exists_domain_eq_top, FiniteArchimedeanClass.addSubgroup_eq_bot, HahnEmbedding.Partial.exists_isMax, HahnEmbedding.Seed.domain_baseEmbedding, FiniteArchimedeanClass.withTopOrderIso_apply_coe, FiniteArchimedeanClass.mem_closedBall_iff, closedBall_top, hahnEmbedding_isOrderedAddMonoid, hahnEmbedding_isOrderedModule, HahnEmbedding.Partial.toOrderAddMonoidHom_injective
liftOrderHom πŸ“–CompOp
1 mathmath: liftOrderHom_mk
liftβ‚‚ πŸ“–CompOp
1 mathmath: liftβ‚‚_mk
mk πŸ“–CompOpβ€”
orderHom πŸ“–CompOp
5 mathmath: orderHom_zero, DivisibleHull.archimedeanClassOrderIso_apply, orderHom_top, orderHom_mk, orderHom_injective
out πŸ“–CompOp
2 mathmath: mk_out, out_top
subsemigroup πŸ“–CompOp
3 mathmath: subsemigroup_eq_addSubgroup_of_ne_top, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, subsemigroup_strictAnti

Theorems

NameKindAssumesProvesValidatesDepends On
addSubgroup_antitone πŸ“–mathematicalβ€”Antitone
UpperSet
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddSubgroup
AddCommGroup.toAddGroup
UpperSet.instPartialOrder
AddSubgroup.instPartialOrder
addSubgroup
β€”eq_or_ne
eq_top_iff
le_refl
addSubgroup_eq_bot
bot_le
StrictAntiOn.le_iff_ge
addSubgroup_strictAntiOn
Ne.lt_top
addSubgroup_eq_bot πŸ“–mathematicalβ€”addSubgroup
Top.top
UpperSet
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
UpperSet.instTop
Bot.bot
AddSubgroup
AddCommGroup.toAddGroup
AddSubgroup.instBot
β€”β€”
addSubgroup_strictAntiOn πŸ“–mathematicalβ€”StrictAntiOn
UpperSet
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddSubgroup
AddCommGroup.toAddGroup
UpperSet.instPartialOrder
AddSubgroup.instPartialOrder
addSubgroup
Set.Iio
Top.top
UpperSet.instTop
β€”SetLike.coe_ssubset_coe
instIsConcreteLE
subsemigroup_eq_addSubgroup_of_ne_top
LT.lt.ne_top
Set.mem_Iio
Set.ssubset_iff_subset_ne
Set.preimage_subset_preimage_iff
Set.subset_univ
UpperSet.coe_subset_coe
LT.lt.le
Mathlib.Tactic.Contrapose.contrapose₃
not_lt
le_of_eq
Set.preimage_eq_preimage
mk_surjective
SetLike.coe_set_eq
archimedean_of_mk_eq_mk πŸ“–mathematicalβ€”Archimedean
AddCommGroup.toAddCommMonoid
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”zero_nsmul
LT.lt.ne
not_le
abs_eq_self
LT.lt.le
ballAddSubgroup_antitone πŸ“–mathematicalβ€”Antitone
ArchimedeanClass
AddSubgroup
AddCommGroup.toAddGroup
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddSubgroup.instPartialOrder
ballAddSubgroup
β€”addSubgroup_antitone
StrictMono.monotone
UpperSet.Ioi_strictMono
ballAddSubgroup_top πŸ“–mathematicalβ€”ballAddSubgroup
Top.top
ArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
Bot.bot
AddSubgroup
AddCommGroup.toAddGroup
AddSubgroup.instBot
β€”UpperSet.Ioi_top
addSubgroup_eq_bot
closedBallAddSubgroup_top πŸ“–mathematicalβ€”closedBallAddSubgroup
Top.top
ArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
Bot.bot
AddSubgroup
AddCommGroup.toAddGroup
AddSubgroup.instBot
β€”AddSubgroup.ext
mem_addSubgroup_iff
UpperSet.Ici_ne_top
UpperSet.mem_Ici_iff
top_le_iff
mk_eq_top_iff
AddSubgroup.mem_bot
forall πŸ“–β€”β€”β€”β€”Quotient.forall
ind πŸ“–β€”β€”β€”β€”Antisymmetrization.ind
instNontrivial πŸ“–mathematicalβ€”Nontrivial
ArchimedeanClass
β€”exists_ne
Iff.ne
mk_eq_top_iff
instSubsingleton πŸ“–mathematicalβ€”ArchimedeanClassβ€”instSubsingletonAntisymmetrization
ArchimedeanOrder.instSubsingleton
liftOrderHom_mk πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
DFunLike.coe
OrderHom
ArchimedeanClass
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
OrderHom.instFunLike
liftOrderHom
β€”le_antisymm
Eq.le
Eq.ge
lift_mk πŸ“–mathematicalβ€”liftβ€”β€”
liftβ‚‚_mk πŸ“–mathematicalβ€”liftβ‚‚β€”β€”
lt_of_mk_lt_mk_of_nonneg πŸ“–β€”ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Preorder.toLE
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”β€”abs_eq_self
abs_lt
IsOrderedAddMonoid.toAddLeftMono
covariant_swap_add_of_covariant_add
one_nsmul
lt_of_mk_lt_mk_of_nonpos πŸ“–β€”ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Preorder.toLE
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”β€”neg_neg
abs_eq_neg_self
abs_lt
IsOrderedAddMonoid.toAddLeftMono
covariant_swap_add_of_covariant_add
one_nsmul
map_mk_eq πŸ“–mathematicalβ€”DFunLike.coe
OrderAddMonoidHom
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
OrderAddMonoidHom.instFunLike
β€”β€”
map_mk_le πŸ“–mathematicalArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DFunLike.coe
OrderAddMonoidHom
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
OrderAddMonoidHom.instFunLike
β€”OrderHomClass.monotone
OrderHom.instOrderHomClass
mem_addSubgroup_iff πŸ“–mathematicalβ€”AddSubgroup
AddCommGroup.toAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addSubgroup
ArchimedeanClass
UpperSet
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
UpperSet.instSetLike
β€”Set.mem_preimage
SetLike.mem_coe
mem_ballAddSubgroup_iff πŸ“–mathematicalβ€”AddSubgroup
AddCommGroup.toAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
ballAddSubgroup
ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
β€”mem_addSubgroup_iff
UpperSet.Ioi_eq_top
UpperSet.mem_Ioi_iff
mem_closedBallAddSubgroup_iff πŸ“–mathematicalβ€”AddSubgroup
AddCommGroup.toAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
closedBallAddSubgroup
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
β€”mem_addSubgroup_iff
UpperSet.Ici_ne_top
UpperSet.mem_Ici_iff
min_le_mk_add πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SemilatticeInf.toMin
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”LT.lt.trans_le
lt_min_iff
not_le
abs_add_le
IsOrderedAddMonoid.toAddLeftMono
LT.lt.not_gt
two_nsmul
add_lt_add_iff_left
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
add_lt_add_iff_right
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
contravariant_swap_add_of_contravariant_add
min_le_mk_of_le_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass
instLinearOrder
SemilatticeInf.toMin
β€”abs_le_max_abs_abs
LE.le.trans'
mk_le_mk_of_abs
abs_of_nonneg
IsOrderedAddMonoid.toAddLeftMono
le_max_of_le_left
abs_nonneg
covariant_swap_add_of_covariant_add
le_total
max_eq_right
min_eq_right
mk_abs
le_refl
max_eq_left
min_eq_left
min_le_mk_sub πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SemilatticeInf.toMin
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_eq_add_neg
inf_le_iff
mk_neg
min_le_mk_add
mk_abs πŸ“–mathematicalβ€”abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddCommGroup.toAddGroup
β€”abs_abs
IsOrderedAddMonoid.toAddLeftMono
covariant_swap_add_of_covariant_add
one_nsmul
le_refl
mk_add_eq_mk_left πŸ“–mathematicalArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”le_antisymm
LE.le.trans
abs_add'
add_comm
two_nsmul
add_le_add_iff_right
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT
AddRightCancelSemigroup.toIsRightCancelAdd
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
le_of_add_le_add_left
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
LT.lt.le
mk_left_le_mk_add
mk_add_eq_mk_right πŸ“–mathematicalArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”mk_add_eq_mk_left
add_comm
mk_add_lt_mk_left_iff πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”le_iff_le_iff_lt_iff_lt
mk_left_le_mk_add_iff
mk_add_lt_mk_right_iff πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”le_iff_le_iff_lt_iff_lt
mk_right_le_mk_add_iff
mk_antitoneOn πŸ“–mathematicalβ€”AntitoneOn
ArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Set.Ici
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”Mathlib.Tactic.Contrapose.contrapose₁
not_le
one_nsmul
abs_eq_self
mk_eq_mk πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
abs
AddCommGroup.toAddGroup
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
β€”Quotient.eq
mk_eq_mk_of_archimedean πŸ“–β€”β€”β€”β€”Archimedean.arch
abs_pos
IsOrderedAddMonoid.toAddLeftMono
mk_eq_top_iff πŸ“–mathematicalβ€”Top.top
ArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”abs_zero
IsOrderedAddMonoid.toAddLeftMono
nsmul_zero
abs_nonpos_iff
covariant_swap_add_of_covariant_add
mk_le_mk πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
abs
AddCommGroup.toAddGroup
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
β€”β€”
mk_le_mk_iff_lt πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Preorder.toLT
abs
AddCommGroup.toAddGroup
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
β€”LE.le.trans_lt
succ_nsmul
lt_add_of_pos_right
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
abs_pos
LT.lt.le
mk_le_mk_of_abs πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
abs
AddCommGroup.toAddGroup
ArchimedeanClass
instLinearOrder
β€”mk_abs
abs_nonneg
IsOrderedAddMonoid.toAddLeftMono
covariant_swap_add_of_covariant_add
mk_antitoneOn
LE.le.trans
mk_left_le_mk_add πŸ“–mathematicalArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”inf_of_le_left
min_le_mk_add
mk_left_le_mk_add_iff πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_add_cancel_left
mk_neg
mk_left_le_mk_sub
mk_left_le_mk_add
mk_left_le_mk_sub πŸ“–mathematicalArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_eq_add_neg
mk_neg
mk_left_le_mk_add
mk_left_le_mk_sub_iff πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_sub_cancel
mk_left_le_mk_sub
mk_lt_mk πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
abs
β€”β€”
mk_monotoneOn πŸ“–mathematicalβ€”MonotoneOn
ArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Set.Iic
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”Mathlib.Tactic.Contrapose.contrapose₁
not_le
one_nsmul
neg_lt_neg_iff
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
abs_eq_neg_self
mk_neg πŸ“–mathematicalβ€”NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”abs_neg
one_nsmul
le_refl
mk_out πŸ“–mathematicalβ€”outβ€”Quotient.out_eq'
mk_right_le_mk_add πŸ“–mathematicalArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”inf_of_le_right
min_le_mk_add
mk_right_le_mk_add_iff πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”add_comm
mk_left_le_mk_add_iff
mk_right_le_mk_sub πŸ“–mathematicalArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_eq_add_neg
mk_neg
mk_right_le_mk_add
mk_right_le_mk_sub_iff πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”mk_sub_comm
mk_left_le_mk_sub_iff
mk_sub_comm πŸ“–mathematicalβ€”SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”mk_neg
neg_sub
mk_sub_eq_mk_left πŸ“–mathematicalArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_eq_add_neg
mk_neg
mk_add_eq_mk_left
mk_sub_eq_mk_right πŸ“–mathematicalArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_eq_add_neg
mk_neg
mk_add_eq_mk_right
mk_sub_lt_mk_left_iff πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”le_iff_le_iff_lt_iff_lt
mk_left_le_mk_sub_iff
mk_sub_lt_mk_right_iff πŸ“–mathematicalβ€”ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”le_iff_le_iff_lt_iff_lt
mk_right_le_mk_sub_iff
mk_sum πŸ“–mathematicalFinset.Nonempty
StrictMonoOn
ArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SetLike.coe
Finset
Finset.instSetLike
Finset.sum
AddCommGroup.toAddCommMonoid
Finset.min'
β€”Finset.Nonempty.cons_induction
Finset.singleton_nonempty
Finset.coe_singleton
Set.strictMonoOn_singleton
Finset.sum_singleton
Finset.min'_singleton
Finset.cons_nonempty
Finset.sum_cons
Finset.mem_cons_of_mem
Finset.min'_mem
StrictMonoOn.injOn
Finset.cons_eq_insert
Finset.coe_insert
Set.mem_insert_iff
SetLike.mem_coe
lt_or_gt_of_ne
StrictMonoOn.mono
Set.subset_insert
mk_add_eq_mk_left
le_antisymm
Finset.mem_insert
Finset.le_min'
Finset.mem_cons
le_refl
LT.lt.le
lt_of_lt_of_le
StrictMonoOn.lt_iff_lt
Finset.min'_le
add_comm
mk_surjective πŸ“–mathematicalβ€”ArchimedeanClassβ€”Quotient.mk_surjective
mk_zero πŸ“–mathematicalβ€”NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Top.top
ArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
β€”β€”
orderHom_injective πŸ“–mathematicalDFunLike.coe
OrderAddMonoidHom
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
OrderAddMonoidHom.instFunLike
ArchimedeanClass
OrderHom
instLinearOrder
OrderHom.instFunLike
orderHom
β€”ind
map_abs
OrderAddMonoidHom.instOrderHomClass
OrderAddMonoidHom.instAddMonoidHomClass
map_nsmul
StrictMono.le_iff_le
Monotone.strictMono_of_injective
OrderHomClass.monotone
orderHom_mk πŸ“–mathematicalβ€”DFunLike.coe
OrderHom
ArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
OrderHom.instFunLike
orderHom
OrderAddMonoidHom
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
OrderAddMonoidHom.instFunLike
β€”β€”
orderHom_top πŸ“–mathematicalβ€”DFunLike.coe
OrderHom
ArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
OrderHom.instFunLike
orderHom
Top.top
OrderTop.toTop
Preorder.toLE
instOrderTop
β€”mk_zero
map_zero
AddMonoidHomClass.toZeroHomClass
OrderAddMonoidHom.instAddMonoidHomClass
out_top πŸ“–mathematicalβ€”out
Top.top
ArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”mk_eq_top_iff
mk_out
pos_of_pos_of_mk_lt πŸ“–β€”Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
ArchimedeanClass
instLinearOrder
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”β€”lt_of_mk_lt_mk_of_nonpos
mk_neg
Left.neg_nonpos_iff
IsOrderedAddMonoid.toAddLeftMono
LT.lt.le
neg_lt_sub_iff_lt_add
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
lt_add_iff_pos_right
contravariant_lt_of_covariant_le
range_mk πŸ“–mathematicalβ€”Set.range
ArchimedeanClass
Set.univ
β€”Set.range_eq_univ
mk_surjective
subsemigroup_eq_addSubgroup_of_ne_top πŸ“–mathematicalβ€”SetLike.coe
AddSubsemigroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddSubsemigroup.instSetLike
subsemigroup
AddSubgroup
AddSubgroup.instSetLike
addSubgroup
β€”β€”
subsemigroup_strictAnti πŸ“–mathematicalβ€”StrictAnti
UpperSet
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
AddSubsemigroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
UpperSet.instPartialOrder
AddSubsemigroup.instPartialOrder
subsemigroup
β€”SetLike.coe_ssubset_coe
instIsConcreteLE
Set.ssubset_iff_subset_ne
LT.lt.le
Mathlib.Tactic.Contrapose.contrapose₃
not_lt
le_of_eq
Set.preimage_eq_preimage
mk_surjective
SetLike.coe_set_eq
top_eq_mk_iff πŸ“–mathematicalβ€”Top.top
ArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”mk_eq_top_iff

ArchimedeanOrder

Definitions

NameCategoryTheorems
instInhabited πŸ“–CompOpβ€”
instLE πŸ“–CompOp
2 mathmath: le_def, instTotalLe
instLT πŸ“–CompOp
1 mathmath: lt_def
instPreorder πŸ“–CompOpβ€”
of πŸ“–CompOp
4 mathmath: val_of, of_val, val_symm_eq, of_symm_eq
orderHom πŸ“–CompOpβ€”
val πŸ“–CompOp
6 mathmath: le_def, val_of, of_val, val_symm_eq, lt_def, of_symm_eq

Theorems

NameKindAssumesProvesValidatesDepends On
instNonempty πŸ“–mathematicalβ€”ArchimedeanOrderβ€”β€”
instSubsingleton πŸ“–mathematicalβ€”ArchimedeanOrderβ€”β€”
instTotalLe πŸ“–mathematicalβ€”ArchimedeanOrder
instLE
AddCommGroup.toAddGroup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”le_total
one_nsmul
le_def πŸ“–mathematicalβ€”ArchimedeanOrder
instLE
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
abs
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
val
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
β€”β€”
lt_def πŸ“–mathematicalβ€”ArchimedeanOrder
instLT
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
abs
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
val
β€”β€”
of_symm_eq πŸ“–mathematicalβ€”Equiv.symm
ArchimedeanOrder
of
val
β€”β€”
of_val πŸ“–mathematicalβ€”DFunLike.coe
Equiv
ArchimedeanOrder
EquivLike.toFunLike
Equiv.instEquivLike
of
val
β€”β€”
val_of πŸ“–mathematicalβ€”DFunLike.coe
Equiv
ArchimedeanOrder
EquivLike.toFunLike
Equiv.instEquivLike
val
of
β€”β€”
val_symm_eq πŸ“–mathematicalβ€”Equiv.symm
ArchimedeanOrder
val
of
β€”β€”

FiniteArchimedeanClass

Definitions

NameCategoryTheorems
addSubgroup πŸ“–CompOp
4 mathmath: mem_addSubgroup_iff, subsemigroup_eq_addSubgroup, addSubgroup_strictAnti, addSubgroup_eq_bot
ballAddSubgroup πŸ“–CompOp
3 mathmath: toAddSubgroup_ball, mem_ballAddSubgroup_iff, ballAddSubgroup_strictAnti
closedBallAddSubgroup πŸ“–CompOp
2 mathmath: mem_closedBallAddSubgroup_iff, toAddSubgroup_closedBall
congrOrderIso πŸ“–CompOp
2 mathmath: congrOrderIso_symm, coe_congrOrderIso_apply
liftOrderHom πŸ“–CompOp
1 mathmath: liftOrderHom_mk
mk πŸ“–CompOpβ€”
toUpperSetAddArchimedeanClass πŸ“–CompOp
1 mathmath: subsemigroup_eq_addSubgroup
withTopOrderIso πŸ“–CompOp
6 mathmath: HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, hahnEmbedding_isOrderedModule_rat, withTopOrderIso_symm_apply, withTopOrderIso_apply_coe, hahnEmbedding_isOrderedAddMonoid, hahnEmbedding_isOrderedModule

Theorems

NameKindAssumesProvesValidatesDepends On
addSubgroup_eq_bot πŸ“–mathematicalβ€”addSubgroup
Top.top
UpperSet
FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
OrderTop.toTop
ArchimedeanClass.instOrderTop
UpperSet.instTop
Bot.bot
AddSubgroup
AddCommGroup.toAddGroup
AddSubgroup.instBot
β€”AddSubgroup.ext
UpperSet.notMem_top
Set.mem_preimage
Set.mem_singleton_iff
ArchimedeanClass.mk_eq_top_iff
AddSubgroup.mem_bot
addSubgroup_strictAnti πŸ“–mathematicalβ€”StrictAnti
UpperSet
FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
AddSubgroup
AddCommGroup.toAddGroup
UpperSet.instPartialOrder
AddSubgroup.instPartialOrder
addSubgroup
β€”ArchimedeanClass.subsemigroup_strictAnti
OrderEmbedding.strictMono
ballAddSubgroup_strictAnti πŸ“–mathematicalβ€”StrictAnti
FiniteArchimedeanClass
AddSubgroup
AddCommGroup.toAddGroup
Subtype.preorder
ArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
ArchimedeanClass.instOrderTop
AddSubgroup.instPartialOrder
ballAddSubgroup
β€”addSubgroup_strictAnti
UpperSet.Ioi_strictMono
coe_congrOrderIso_apply πŸ“–mathematicalβ€”ArchimedeanClass
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
ArchimedeanClass.instOrderTop
DFunLike.coe
OrderIso
FiniteArchimedeanClass
instFunLikeOrderIso
congrOrderIso
β€”β€”
congrOrderIso_symm πŸ“–mathematicalβ€”OrderIso.symm
FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
congrOrderIso
β€”β€”
ind πŸ“–β€”β€”β€”β€”ArchimedeanClass.mk_eq_top_iff
ArchimedeanClass.forall
instNonemptyOfNontrivial πŸ“–mathematicalβ€”FiniteArchimedeanClassβ€”exists_ne
ArchimedeanClass.mk_eq_top_iff
instSubsingletonOfAddArchimedean πŸ“–mathematicalβ€”FiniteArchimedeanClassβ€”ind
ArchimedeanClass.mk_eq_mk_of_archimedean
liftOrderHom_mk πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
DFunLike.coe
OrderHom
FiniteArchimedeanClass
Subtype.preorder
ArchimedeanClass
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
OrderHom.instFunLike
liftOrderHom
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”Subtype.prop
le_antisymm
Eq.le
Eq.ge
lift_mk πŸ“–mathematicalβ€”lift
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”Subtype.prop
WithTop.untop.congr_simp
ArchimedeanClass.lift.congr_simp
mem_addSubgroup_iff πŸ“–mathematicalβ€”AddSubgroup
AddCommGroup.toAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
addSubgroup
FiniteArchimedeanClass
UpperSet
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
UpperSet.instSetLike
β€”ArchimedeanClass.mk_eq_top_iff
mem_ballAddSubgroup_iff πŸ“–mathematicalβ€”AddSubgroup
AddCommGroup.toAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
ballAddSubgroup
FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
ArchimedeanClass.instOrderTop
β€”mem_addSubgroup_iff
UpperSet.mem_Ioi_iff
mem_closedBallAddSubgroup_iff πŸ“–mathematicalβ€”AddSubgroup
AddCommGroup.toAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
closedBallAddSubgroup
FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
β€”mem_addSubgroup_iff
UpperSet.mem_Ici_iff
min_le_mk_add πŸ“–mathematicalβ€”FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
SemilatticeInf.toMin
instIsLinearOrder_mathlib
instLawfulOrderInf_mathlib
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”ArchimedeanClass.min_le_mk_add
mk_le_mk πŸ“–mathematicalβ€”FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
β€”β€”
mk_lt_mk πŸ“–mathematicalβ€”FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
ArchimedeanClass.instOrderTop
β€”β€”
mk_neg πŸ“–mathematicalβ€”NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”ArchimedeanClass.mk_neg
subsemigroup_eq_addSubgroup πŸ“–mathematicalβ€”SetLike.coe
AddSubsemigroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddSubsemigroup.instSetLike
ArchimedeanClass.subsemigroup
DFunLike.coe
OrderEmbedding
UpperSet
FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
UpperSet.instPartialOrder
instFunLikeOrderEmbedding
toUpperSetAddArchimedeanClass
AddSubgroup
AddSubgroup.instSetLike
addSubgroup
β€”β€”
val_mk πŸ“–mathematicalβ€”ArchimedeanClass
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
ArchimedeanClass.instOrderTop
β€”β€”
withTopOrderIso_apply_coe πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
WithTop
FiniteArchimedeanClass
ArchimedeanClass
Preorder.toLE
WithTop.instPreorder
Subtype.preorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
instFunLikeOrderIso
withTopOrderIso
WithTop.some
β€”WithTop.subtypeOrderIso_apply_coe
withTopOrderIso_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
ArchimedeanClass
WithTop
FiniteArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ArchimedeanClass.instLinearOrder
WithTop.instPreorder
Subtype.preorder
Top.top
OrderTop.toTop
ArchimedeanClass.instOrderTop
instFunLikeOrderIso
OrderIso.symm
withTopOrderIso
WithTop.some
β€”WithTop.subtypeOrderIso_symm_apply
Iff.ne
ArchimedeanClass.mk_eq_top_iff

FiniteMulArchimedeanClass

Definitions

NameCategoryTheorems
ballSubgroup πŸ“–CompOp
2 mathmath: mem_ballSubgroup_iff, ballSubgroup_strictAnti
closedBallSubgroup πŸ“–CompOp
1 mathmath: mem_closedBallSubgroup_iff
congrOrderIso πŸ“–CompOp
2 mathmath: congrOrderIso_symm, coe_congrOrderIso_apply
liftOrderHom πŸ“–CompOp
1 mathmath: liftOrderHom_mk
mk πŸ“–CompOpβ€”
subgroup πŸ“–CompOp
4 mathmath: mem_subgroup_iff, subgroup_eq_bot, subsemigroup_eq_subgroup, subgroup_strictAnti
toUpperSetMulArchimedeanClass πŸ“–CompOp
1 mathmath: subsemigroup_eq_subgroup
withTopOrderIso πŸ“–CompOp
2 mathmath: withTopOrderIso_apply_coe, withTopOrderIso_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
ballSubgroup_strictAnti πŸ“–mathematicalβ€”StrictAnti
FiniteMulArchimedeanClass
Subgroup
CommGroup.toGroup
Subtype.preorder
MulArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
MulArchimedeanClass.instOrderTop
Subgroup.instPartialOrder
ballSubgroup
β€”subgroup_strictAnti
UpperSet.Ioi_strictMono
coe_congrOrderIso_apply πŸ“–mathematicalβ€”MulArchimedeanClass
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
MulArchimedeanClass.instOrderTop
DFunLike.coe
OrderIso
FiniteMulArchimedeanClass
instFunLikeOrderIso
congrOrderIso
β€”β€”
congrOrderIso_symm πŸ“–mathematicalβ€”OrderIso.symm
FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
congrOrderIso
β€”β€”
ind πŸ“–β€”β€”β€”β€”β€”
instNonemptyOfNontrivial πŸ“–mathematicalβ€”FiniteMulArchimedeanClassβ€”exists_ne
instSubsingletonOfMulArchimedean πŸ“–mathematicalβ€”FiniteMulArchimedeanClassβ€”ind
MulArchimedeanClass.mk_eq_mk_of_mulArchimedean
liftOrderHom_mk πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
DFunLike.coe
OrderHom
FiniteMulArchimedeanClass
Subtype.preorder
MulArchimedeanClass
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
OrderHom.instFunLike
liftOrderHom
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”Subtype.prop
le_antisymm
Eq.le
Eq.ge
lift_mk πŸ“–mathematicalβ€”lift
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”Subtype.prop
WithTop.untop.congr_simp
MulArchimedeanClass.lift.congr_simp
mem_ballSubgroup_iff πŸ“–mathematicalβ€”Subgroup
CommGroup.toGroup
SetLike.instMembership
Subgroup.instSetLike
ballSubgroup
FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
MulArchimedeanClass.instOrderTop
β€”β€”
mem_closedBallSubgroup_iff πŸ“–mathematicalβ€”Subgroup
CommGroup.toGroup
SetLike.instMembership
Subgroup.instSetLike
closedBallSubgroup
FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
β€”β€”
mem_subgroup_iff πŸ“–mathematicalβ€”Subgroup
CommGroup.toGroup
SetLike.instMembership
Subgroup.instSetLike
subgroup
FiniteMulArchimedeanClass
UpperSet
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
UpperSet.instSetLike
β€”β€”
min_le_mk_mul πŸ“–mathematicalβ€”FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
SemilatticeInf.toMin
instIsLinearOrder_mathlib
instLawfulOrderInf_mathlib
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”MulArchimedeanClass.min_le_mk_mul
mk_inv πŸ“–mathematicalβ€”InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”MulArchimedeanClass.mk_inv
mk_le_mk πŸ“–mathematicalβ€”FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
β€”β€”
mk_lt_mk πŸ“–mathematicalβ€”FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
MulArchimedeanClass.instOrderTop
β€”β€”
subgroup_eq_bot πŸ“–mathematicalβ€”subgroup
Top.top
UpperSet
FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
OrderTop.toTop
MulArchimedeanClass.instOrderTop
UpperSet.instTop
Bot.bot
Subgroup
CommGroup.toGroup
Subgroup.instBot
β€”Subgroup.ext
subgroup_strictAnti πŸ“–mathematicalβ€”StrictAnti
UpperSet
FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
Subgroup
CommGroup.toGroup
UpperSet.instPartialOrder
Subgroup.instPartialOrder
subgroup
β€”MulArchimedeanClass.subsemigroup_strictAnti
OrderEmbedding.strictMono
subsemigroup_eq_subgroup πŸ“–mathematicalβ€”SetLike.coe
Subsemigroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
Subsemigroup.instSetLike
MulArchimedeanClass.subsemigroup
DFunLike.coe
OrderEmbedding
UpperSet
FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
UpperSet.instPartialOrder
instFunLikeOrderEmbedding
toUpperSetMulArchimedeanClass
Subgroup
Subgroup.instSetLike
subgroup
β€”β€”
val_mk πŸ“–mathematicalβ€”MulArchimedeanClass
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
MulArchimedeanClass.instOrderTop
β€”β€”
withTopOrderIso_apply_coe πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
WithTop
FiniteMulArchimedeanClass
MulArchimedeanClass
Preorder.toLE
WithTop.instPreorder
Subtype.preorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
instFunLikeOrderIso
withTopOrderIso
WithTop.some
β€”WithTop.subtypeOrderIso_apply_coe
withTopOrderIso_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
MulArchimedeanClass
WithTop
FiniteMulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass.instLinearOrder
WithTop.instPreorder
Subtype.preorder
Top.top
OrderTop.toTop
MulArchimedeanClass.instOrderTop
instFunLikeOrderIso
OrderIso.symm
withTopOrderIso
WithTop.some
β€”WithTop.subtypeOrderIso_symm_apply
Iff.ne
MulArchimedeanClass.mk_eq_top_iff

MulArchimedeanClass

Definitions

NameCategoryTheorems
ballSubgroup πŸ“–CompOp
3 mathmath: ballSubgroup_antitone, ballSubgroup_top, mem_ballSubgroup_iff
closedBallSubgroup πŸ“–CompOp
2 mathmath: mem_closedBallSubgroup_iff, closedBallSubgroup_top
instInhabited πŸ“–CompOpβ€”
instLinearOrder πŸ“–CompOp
51 mathmath: subgroup_strictAntiOn, orderHom_injective, top_eq_mk_iff, mk_left_le_mk_mul_iff, mem_subgroup_iff, subsemigroup_strictAnti, mk_lt_mk, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, liftOrderHom_mk, min_le_mk_mul, mem_closedBallSubgroup_iff, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, mk_mul_lt_mk_left_iff, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, mk_le_mk_iff_lt, FiniteMulArchimedeanClass.liftOrderHom_mk, mk_antitoneOn, mk_monotoneOn, ballSubgroup_antitone, mk_div_lt_mk_left_iff, mk_right_le_mk_mul_iff, mk_one, FiniteMulArchimedeanClass.mk_le_mk, FiniteMulArchimedeanClass.mem_subgroup_iff, FiniteMulArchimedeanClass.congrOrderIso_symm, FiniteMulArchimedeanClass.min_le_mk_mul, mk_mul_lt_mk_right_iff, out_top, mk_left_le_mk_div_iff, ballSubgroup_top, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, mem_ballSubgroup_iff, FiniteMulArchimedeanClass.subgroup_eq_bot, subgroup_antitone, closedBallSubgroup_top, mk_le_mk, mk_eq_top_iff, mk_le_mk_of_mabs, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, FiniteMulArchimedeanClass.val_mk, FiniteMulArchimedeanClass.mk_lt_mk, mk_right_le_mk_div_iff, orderHom_mk, min_le_mk_div, FiniteMulArchimedeanClass.subgroup_strictAnti, subgroup_eq_bot, mk_div_lt_mk_right_iff, min_le_mk_of_le_of_le, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, orderHom_top
instOrderTop πŸ“–CompOp
23 mathmath: top_eq_mk_iff, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, FiniteMulArchimedeanClass.liftOrderHom_mk, mk_one, FiniteMulArchimedeanClass.mk_le_mk, FiniteMulArchimedeanClass.mem_subgroup_iff, FiniteMulArchimedeanClass.congrOrderIso_symm, FiniteMulArchimedeanClass.min_le_mk_mul, out_top, ballSubgroup_top, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, FiniteMulArchimedeanClass.subgroup_eq_bot, closedBallSubgroup_top, mk_eq_top_iff, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, FiniteMulArchimedeanClass.val_mk, FiniteMulArchimedeanClass.mk_lt_mk, FiniteMulArchimedeanClass.subgroup_strictAnti, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, orderHom_top
liftOrderHom πŸ“–CompOp
1 mathmath: liftOrderHom_mk
liftβ‚‚ πŸ“–CompOp
1 mathmath: liftβ‚‚_mk
mk πŸ“–CompOpβ€”
orderHom πŸ“–CompOp
3 mathmath: orderHom_injective, orderHom_mk, orderHom_top
out πŸ“–CompOp
2 mathmath: out_top, mk_out
subgroup πŸ“–CompOp
5 mathmath: subgroup_strictAntiOn, mem_subgroup_iff, subsemigroup_eq_subgroup_of_ne_top, subgroup_antitone, subgroup_eq_bot
subsemigroup πŸ“–CompOp
3 mathmath: subsemigroup_strictAnti, subsemigroup_eq_subgroup_of_ne_top, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup

Theorems

NameKindAssumesProvesValidatesDepends On
ballSubgroup_antitone πŸ“–mathematicalβ€”Antitone
MulArchimedeanClass
Subgroup
CommGroup.toGroup
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Subgroup.instPartialOrder
ballSubgroup
β€”subgroup_antitone
StrictMono.monotone
UpperSet.Ioi_strictMono
ballSubgroup_top πŸ“–mathematicalβ€”ballSubgroup
Top.top
MulArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
Bot.bot
Subgroup
CommGroup.toGroup
Subgroup.instBot
β€”UpperSet.Ioi_top
subgroup_eq_bot
closedBallSubgroup_top πŸ“–mathematicalβ€”closedBallSubgroup
Top.top
MulArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
Bot.bot
Subgroup
CommGroup.toGroup
Subgroup.instBot
β€”Subgroup.ext
forall πŸ“–β€”β€”β€”β€”Quotient.forall
ind πŸ“–β€”β€”β€”β€”Antisymmetrization.ind
instNontrivial πŸ“–mathematicalβ€”Nontrivial
MulArchimedeanClass
β€”exists_ne
Iff.ne
mk_eq_top_iff
instSubsingleton πŸ“–mathematicalβ€”MulArchimedeanClassβ€”instSubsingletonAntisymmetrization
MulArchimedeanOrder.instSubsingleton
liftOrderHom_mk πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
DFunLike.coe
OrderHom
MulArchimedeanClass
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
OrderHom.instFunLike
liftOrderHom
β€”le_antisymm
Eq.le
Eq.ge
lift_mk πŸ“–mathematicalβ€”liftβ€”β€”
liftβ‚‚_mk πŸ“–mathematicalβ€”liftβ‚‚β€”β€”
lt_of_mk_lt_mk_of_le_one πŸ“–β€”MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Preorder.toLE
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”β€”inv_inv
mabs_eq_inv_self
mabs_lt
IsOrderedMonoid.toMulLeftMono
covariant_swap_mul_of_covariant_mul
pow_one
lt_of_mk_lt_mk_of_one_le πŸ“–β€”MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Preorder.toLE
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”β€”mabs_eq_self
mabs_lt
IsOrderedMonoid.toMulLeftMono
covariant_swap_mul_of_covariant_mul
pow_one
map_mk_eq πŸ“–mathematicalβ€”DFunLike.coe
OrderMonoidHom
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
OrderMonoidHom.instFunLike
β€”β€”
map_mk_le πŸ“–mathematicalMulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DFunLike.coe
OrderMonoidHom
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
OrderMonoidHom.instFunLike
β€”OrderHomClass.monotone
OrderHom.instOrderHomClass
mem_ballSubgroup_iff πŸ“–mathematicalβ€”Subgroup
CommGroup.toGroup
SetLike.instMembership
Subgroup.instSetLike
ballSubgroup
MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
β€”β€”
mem_closedBallSubgroup_iff πŸ“–mathematicalβ€”Subgroup
CommGroup.toGroup
SetLike.instMembership
Subgroup.instSetLike
closedBallSubgroup
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
β€”β€”
mem_subgroup_iff πŸ“–mathematicalβ€”Subgroup
CommGroup.toGroup
SetLike.instMembership
Subgroup.instSetLike
subgroup
MulArchimedeanClass
UpperSet
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
UpperSet.instSetLike
β€”β€”
min_le_mk_div πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SemilatticeInf.toMin
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”div_eq_mul_inv
mk_inv
min_le_mk_mul
min_le_mk_mul πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SemilatticeInf.toMin
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”LT.lt.trans_le
lt_min_iff
mabs_mul_le
IsOrderedMonoid.toMulLeftMono
LT.lt.not_gt
pow_two
IsLeftCancelMul.mulLeftStrictMono_of_mulLeftMono
LeftCancelSemigroup.toIsLeftCancelMul
contravariant_lt_of_covariant_le
IsRightCancelMul.mulRightStrictMono_of_mulRightMono
RightCancelSemigroup.toIsRightCancelMul
covariant_swap_mul_of_covariant_mul
contravariant_swap_mul_of_contravariant_mul
min_le_mk_of_le_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulArchimedeanClass
instLinearOrder
SemilatticeInf.toMin
β€”mabs_le_max_mabs_mabs
LE.le.trans'
mk_le_mk_of_mabs
mabs_of_one_le
IsOrderedMonoid.toMulLeftMono
le_max_of_le_left
one_le_mabs
covariant_swap_mul_of_covariant_mul
le_total
max_eq_right
min_eq_right
mk_mabs
le_refl
max_eq_left
min_eq_left
mk_antitoneOn πŸ“–mathematicalβ€”AntitoneOn
MulArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Set.Ici
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”Mathlib.Tactic.Contrapose.contrapose₁
pow_one
mabs_eq_self
mk_div_comm πŸ“–mathematicalβ€”DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”mk_inv
inv_div
mk_div_eq_mk_left πŸ“–mathematicalMulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”div_eq_mul_inv
mk_inv
mk_mul_eq_mk_left
mk_div_eq_mk_right πŸ“–mathematicalMulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”div_eq_mul_inv
mk_inv
mk_mul_eq_mk_right
mk_div_lt_mk_left_iff πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”le_iff_le_iff_lt_iff_lt
mk_left_le_mk_div_iff
mk_div_lt_mk_right_iff πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”le_iff_le_iff_lt_iff_lt
mk_right_le_mk_div_iff
mk_eq_mk πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
mabs
CommGroup.toGroup
Monoid.toNatPow
DivInvMonoid.toMonoid
Group.toDivInvMonoid
β€”Quotient.eq
mk_eq_mk_of_mulArchimedean πŸ“–β€”β€”β€”β€”MulArchimedean.arch
IsOrderedMonoid.toMulLeftMono
mk_eq_top_iff πŸ“–mathematicalβ€”Top.top
MulArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”mabs_one
IsOrderedMonoid.toMulLeftMono
one_pow
covariant_swap_mul_of_covariant_mul
mk_inv πŸ“–mathematicalβ€”InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”mabs_inv
pow_one
mk_le_mk πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
mabs
CommGroup.toGroup
Monoid.toNatPow
DivInvMonoid.toMonoid
Group.toDivInvMonoid
β€”β€”
mk_le_mk_iff_lt πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Preorder.toLT
mabs
CommGroup.toGroup
Monoid.toNatPow
DivInvMonoid.toMonoid
Group.toDivInvMonoid
β€”LE.le.trans_lt
pow_succ
lt_mul_of_one_lt_right'
IsLeftCancelMul.mulLeftStrictMono_of_mulLeftMono
LeftCancelSemigroup.toIsLeftCancelMul
IsOrderedMonoid.toMulLeftMono
one_lt_mabs
LT.lt.le
mk_le_mk_of_mabs πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
mabs
CommGroup.toGroup
MulArchimedeanClass
instLinearOrder
β€”mk_mabs
one_le_mabs
IsOrderedMonoid.toMulLeftMono
covariant_swap_mul_of_covariant_mul
mk_antitoneOn
LE.le.trans
mk_left_le_mk_div πŸ“–mathematicalMulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”div_eq_mul_inv
mk_inv
mk_left_le_mk_mul
mk_left_le_mk_div_iff πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”div_div_cancel
mk_left_le_mk_div
mk_left_le_mk_mul πŸ“–mathematicalMulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”inf_of_le_left
min_le_mk_mul
mk_left_le_mk_mul_iff πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”div_mul_cancel_left
mk_inv
mk_left_le_mk_div
mk_left_le_mk_mul
mk_lt_mk πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Monoid.toNatPow
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
mabs
β€”β€”
mk_mabs πŸ“–mathematicalβ€”mabs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
CommGroup.toGroup
β€”mabs_mabs
IsOrderedMonoid.toMulLeftMono
covariant_swap_mul_of_covariant_mul
pow_one
mk_monotoneOn πŸ“–mathematicalβ€”MonotoneOn
MulArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Set.Iic
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”Mathlib.Tactic.Contrapose.contrapose₁
pow_one
IsLeftCancelMul.mulLeftStrictMono_of_mulLeftMono
LeftCancelSemigroup.toIsLeftCancelMul
IsOrderedMonoid.toMulLeftMono
IsRightCancelMul.mulRightStrictMono_of_mulRightMono
RightCancelSemigroup.toIsRightCancelMul
covariant_swap_mul_of_covariant_mul
mabs_eq_inv_self
mk_mul_eq_mk_left πŸ“–mathematicalMulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”le_antisymm
LE.le.trans
mabs_mul'
mul_comm
pow_two
mul_le_mul_iff_right
covariant_swap_mul_of_covariant_mul
IsOrderedMonoid.toMulLeftMono
IsRightCancelMul.mulRightReflectLE_of_mulRightReflectLT
RightCancelSemigroup.toIsRightCancelMul
contravariant_swap_mul_of_contravariant_mul
contravariant_lt_of_covariant_le
le_of_mul_le_mul_left'
IsLeftCancelMul.mulLeftReflectLE_of_mulLeftReflectLT
LeftCancelSemigroup.toIsLeftCancelMul
LT.lt.le
mk_left_le_mk_mul
mk_mul_eq_mk_right πŸ“–mathematicalMulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”mk_mul_eq_mk_left
mul_comm
mk_mul_lt_mk_left_iff πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”le_iff_le_iff_lt_iff_lt
mk_left_le_mk_mul_iff
mk_mul_lt_mk_right_iff πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”le_iff_le_iff_lt_iff_lt
mk_right_le_mk_mul_iff
mk_one πŸ“–mathematicalβ€”InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
Top.top
MulArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
β€”β€”
mk_out πŸ“–mathematicalβ€”outβ€”Quotient.out_eq'
mk_prod πŸ“–mathematicalFinset.Nonempty
StrictMonoOn
MulArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
SetLike.coe
Finset
Finset.instSetLike
Finset.prod
CommGroup.toCommMonoid
Finset.min'
β€”Finset.Nonempty.cons_induction
Finset.singleton_nonempty
Finset.coe_singleton
Finset.prod_singleton
Finset.min'_singleton
Finset.cons_nonempty
Finset.prod_cons
Finset.mem_cons_of_mem
Finset.min'_mem
StrictMonoOn.injOn
Finset.cons_eq_insert
Finset.coe_insert
lt_or_gt_of_ne
StrictMonoOn.mono
mk_mul_eq_mk_left
le_antisymm
Finset.le_min'
Finset.mem_cons
le_refl
LT.lt.le
lt_of_lt_of_le
StrictMonoOn.lt_iff_lt
Finset.min'_le
mul_comm
mk_right_le_mk_div πŸ“–mathematicalMulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”div_eq_mul_inv
mk_inv
mk_right_le_mk_mul
mk_right_le_mk_div_iff πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”mk_div_comm
mk_left_le_mk_div_iff
mk_right_le_mk_mul πŸ“–mathematicalMulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”inf_of_le_right
min_le_mk_mul
mk_right_le_mk_mul_iff πŸ“–mathematicalβ€”MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”mul_comm
mk_left_le_mk_mul_iff
mk_surjective πŸ“–mathematicalβ€”MulArchimedeanClassβ€”Quotient.mk_surjective
mulArchimedean_of_mk_eq_mk πŸ“–mathematicalβ€”MulArchimedean
CommGroup.toCommMonoid
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”pow_zero
LT.lt.ne
mabs_eq_self
LT.lt.le
one_lt_of_one_lt_of_mk_lt πŸ“–β€”Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
MulArchimedeanClass
instLinearOrder
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”β€”lt_of_mk_lt_mk_of_le_one
mk_inv
IsOrderedMonoid.toMulLeftMono
LT.lt.le
IsLeftCancelMul.mulLeftStrictMono_of_mulLeftMono
LeftCancelSemigroup.toIsLeftCancelMul
IsRightCancelMul.mulRightStrictMono_of_mulRightMono
RightCancelSemigroup.toIsRightCancelMul
covariant_swap_mul_of_covariant_mul
contravariant_lt_of_covariant_le
orderHom_injective πŸ“–mathematicalDFunLike.coe
OrderMonoidHom
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
OrderMonoidHom.instFunLike
MulArchimedeanClass
OrderHom
instLinearOrder
OrderHom.instFunLike
orderHom
β€”ind
OrderMonoidHom.instOrderHomClass
OrderMonoidHom.instMonoidHomClass
StrictMono.le_iff_le
Monotone.strictMono_of_injective
OrderHomClass.monotone
orderHom_mk πŸ“–mathematicalβ€”DFunLike.coe
OrderHom
MulArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
OrderHom.instFunLike
orderHom
OrderMonoidHom
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
OrderMonoidHom.instFunLike
β€”β€”
orderHom_top πŸ“–mathematicalβ€”DFunLike.coe
OrderHom
MulArchimedeanClass
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
OrderHom.instFunLike
orderHom
Top.top
OrderTop.toTop
Preorder.toLE
instOrderTop
β€”mk_one
map_one
MonoidHomClass.toOneHomClass
OrderMonoidHom.instMonoidHomClass
out_top πŸ“–mathematicalβ€”out
Top.top
MulArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”mk_eq_top_iff
mk_out
range_mk πŸ“–mathematicalβ€”Set.range
MulArchimedeanClass
Set.univ
β€”Set.range_eq_univ
mk_surjective
subgroup_antitone πŸ“–mathematicalβ€”Antitone
UpperSet
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Subgroup
CommGroup.toGroup
UpperSet.instPartialOrder
Subgroup.instPartialOrder
subgroup
β€”eq_or_ne
eq_top_iff
le_refl
subgroup_eq_bot
StrictAntiOn.le_iff_ge
subgroup_strictAntiOn
Ne.lt_top
subgroup_eq_bot πŸ“–mathematicalβ€”subgroup
Top.top
UpperSet
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
UpperSet.instTop
Bot.bot
Subgroup
CommGroup.toGroup
Subgroup.instBot
β€”β€”
subgroup_strictAntiOn πŸ“–mathematicalβ€”StrictAntiOn
UpperSet
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Subgroup
CommGroup.toGroup
UpperSet.instPartialOrder
Subgroup.instPartialOrder
subgroup
Set.Iio
Top.top
UpperSet.instTop
β€”SetLike.coe_ssubset_coe
instIsConcreteLE
subsemigroup_eq_subgroup_of_ne_top
LT.lt.ne_top
Set.mem_Iio
Set.ssubset_iff_subset_ne
LT.lt.le
Mathlib.Tactic.Contrapose.contrapose₃
le_of_eq
subsemigroup_eq_subgroup_of_ne_top πŸ“–mathematicalβ€”SetLike.coe
Subsemigroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
Subsemigroup.instSetLike
subsemigroup
Subgroup
Subgroup.instSetLike
subgroup
β€”β€”
subsemigroup_strictAnti πŸ“–mathematicalβ€”StrictAnti
UpperSet
MulArchimedeanClass
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
Subsemigroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
UpperSet.instPartialOrder
Subsemigroup.instPartialOrder
subsemigroup
β€”SetLike.coe_ssubset_coe
instIsConcreteLE
Set.ssubset_iff_subset_ne
LT.lt.le
Mathlib.Tactic.Contrapose.contrapose₃
le_of_eq
top_eq_mk_iff πŸ“–mathematicalβ€”Top.top
MulArchimedeanClass
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrder
instOrderTop
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”mk_eq_top_iff

MulArchimedeanOrder

Definitions

NameCategoryTheorems
instInhabited πŸ“–CompOpβ€”
instLE πŸ“–CompOp
2 mathmath: instTotalLe, le_def
instLT πŸ“–CompOp
1 mathmath: lt_def
instPreorder πŸ“–CompOpβ€”
of πŸ“–CompOp
4 mathmath: val_symm_eq, of_symm_eq, of_val, val_of
orderHom πŸ“–CompOpβ€”
val πŸ“–CompOp
6 mathmath: val_symm_eq, of_symm_eq, lt_def, of_val, le_def, val_of

Theorems

NameKindAssumesProvesValidatesDepends On
instNonempty πŸ“–mathematicalβ€”MulArchimedeanOrderβ€”β€”
instSubsingleton πŸ“–mathematicalβ€”MulArchimedeanOrderβ€”β€”
instTotalLe πŸ“–mathematicalβ€”MulArchimedeanOrder
instLE
CommGroup.toGroup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”le_total
pow_one
le_def πŸ“–mathematicalβ€”MulArchimedeanOrder
instLE
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
mabs
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
val
Monoid.toNatPow
DivInvMonoid.toMonoid
Group.toDivInvMonoid
β€”β€”
lt_def πŸ“–mathematicalβ€”MulArchimedeanOrder
instLT
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Monoid.toNatPow
DivInvMonoid.toMonoid
Group.toDivInvMonoid
mabs
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
val
β€”β€”
of_symm_eq πŸ“–mathematicalβ€”Equiv.symm
MulArchimedeanOrder
of
val
β€”β€”
of_val πŸ“–mathematicalβ€”DFunLike.coe
Equiv
MulArchimedeanOrder
EquivLike.toFunLike
Equiv.instEquivLike
of
val
β€”β€”
val_of πŸ“–mathematicalβ€”DFunLike.coe
Equiv
MulArchimedeanOrder
EquivLike.toFunLike
Equiv.instEquivLike
val
of
β€”β€”
val_symm_eq πŸ“–mathematicalβ€”Equiv.symm
MulArchimedeanOrder
val
of
β€”β€”

(root)

Definitions

NameCategoryTheorems
ArchimedeanClass πŸ“–CompOp
145 mathmath: HahnEmbedding.IsPartial.baseEmbedding_le, FiniteArchimedeanClass.mem_addSubgroup_iff, ArchimedeanClass.mk_intCast, ArchimedeanClass.closedBallAddSubgroup_top, ArchimedeanClass.addSubgroup_antitone, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, ArchimedeanClass.min_le_mk_of_le_of_le, FiniteArchimedeanClass.mk_lt_mk, ArchimedeanClass.FiniteResidueField.mk_eq_zero, ArchimedeanClass.mk_pow, ArchimedeanClass.isAddRegular_mk, ArchimedeanClass.mk_le_mk, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, ArchimedeanClass.mk_natCast, HahnEmbedding.Seed.baseEmbedding_strictMono, FiniteArchimedeanClass.val_mk, ArchimedeanClass.mk_add_lt_mk_left_iff, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, ArchimedeanClass.mk_left_le_mk_sub_iff, ArchimedeanClass.mk_le_mk_smul, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, ArchimedeanClass.FiniteElement.val_add, Hyperreal.archimdeanClassMk_coe, HahnEmbedding.Partial.isWF_support_evalCoeff, HahnEmbedding.Partial.orderTop_eq_iff, ArchimedeanClass.top_eq_mk_iff, ArchimedeanClass.instIsOrderedAddMonoid, ArchimedeanClass.mk_ofNat, ArchimedeanClass.mk_lt_mk, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, ArchimedeanClass.orderHom_zero, ArchimedeanClass.mem_ball_iff, ArchimedeanClass.mk_monotoneOn, ArchimedeanClass.instSubsingleton, ArchimedeanClass.mk_sub_lt_mk_right_iff, HahnEmbedding.IsPartial.strictMono, ArchimedeanClass.mk_add_lt_mk_right_iff, ArchimedeanClass.ballAddSubgroup_top, ArchimedeanClass.FiniteElement.val_mul, FiniteArchimedeanClass.liftOrderHom_mk, ArchimedeanClass.mk_map_nonneg_of_archimedean, HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratum, HahnEmbedding.IsPartial.truncLT_mem_range, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, ArchimedeanClass.mk_natCast_nonneg, ArchimedeanClass.mk_right_le_mk_sub_iff, ArchimedeanClass.mk_zero, Hyperreal.archimedeanClassMk_pos_of_tendsto, ArchimedeanClass.FiniteElement.val_sub, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, FiniteArchimedeanClass.mem_ball_iff, ArchimedeanClass.min_le_mk_add, ArchimedeanClass.mk_le_mk_iff_lt, HahnEmbedding.Partial.eval_smul, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, ArchimedeanClass.mem_addSubgroup_iff, ArchimedeanClass.addSubgroup_eq_bot, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, ArchimedeanClass.mk_mul, ArchimedeanClass.instNontrivial, ArchimedeanClass.mk_le_mk_of_abs, ArchimedeanClass.mk_left_le_mk_add_iff, ArchimedeanClass.range_mk, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, ArchimedeanClass.mk_ratCast, ArchimedeanClass.ballAddSubgroup_antitone, ArchimedeanClass.out_top, ArchimedeanClass.subsemigroup_strictAnti, ArchimedeanClass.FiniteElement.val_zero, ArchimedeanClass.ball_top, FiniteArchimedeanClass.mk_le_mk, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, ArchimedeanClass.FiniteResidueField.mk_ne_zero, HahnSeries.archimedeanClassOrderIsoWithTop_apply, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff_of_orderTop_ofLex, ArchimedeanClass.mk_le_mk_iff_ratCast, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', ArchimedeanClass.FiniteElement.val_one, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, ArchimedeanClass.mk_le_mk_iff_denselyOrdered, hahnEmbedding_isOrderedModule_rat, FiniteArchimedeanClass.congrOrderIso_symm, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, ArchimedeanClass.mk_surjective, FiniteArchimedeanClass.withTopOrderIso_symm_apply, HahnEmbedding.Partial.mem_domain, HahnEmbedding.Seed.mem_domain_baseEmbedding, ArchimedeanClass.mk_intCast_nonneg, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, DivisibleHull.archimedeanClassOrderIso_apply, Hyperreal.archimedeanClassMk_omega_neg, Hyperreal.archimedeanClassMk_coe_nonneg, ArchimedeanClass.mem_closedBall_iff, ArchimedeanClass.mk_ratCast_nonneg, Hyperreal.tendsto_atBot_iff, FiniteArchimedeanClass.addSubgroup_strictAnti, ArchimedeanClass.mk_le_mk_add_of_archimedean, ArchimedeanClass.mk_nonneg_of_le_of_le_of_archimedean, FiniteArchimedeanClass.coe_congrOrderIso_apply, ArchimedeanClass.mk_eq_top_iff, ArchimedeanClass.mk_le_add_mk_of_archimedean, ArchimedeanClass.mk_right_le_mk_add_iff, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, DivisibleHull.archimedeanClassOrderIso_symm_apply, ArchimedeanClass.addSubgroup_strictAntiOn, FiniteArchimedeanClass.submodule_strictAnti, ArchimedeanClass.mk_one, ArchimedeanClass.mem_ballAddSubgroup_iff, ArchimedeanClass.min_le_mk_sub, ArchimedeanClass.eq_zero_or_top_of_archimedean, FiniteArchimedeanClass.ball_strictAnti, ArchimedeanClass.orderHom_top, HahnEmbedding.Partial.eval_zero, HahnSeries.finiteArchimedeanClassOrderIso_apply, FiniteArchimedeanClass.min_le_mk_add, ArchimedeanClass.liftOrderHom_mk, ArchimedeanClass.orderHom_mk, ArchimedeanClass.mk_div, ArchimedeanClass.addValuation_apply, ArchimedeanClass.mk_antitoneOn, HahnEmbedding.Partial.exists_domain_eq_top, ArchimedeanClass.mk_eq_zero_of_archimedean, ArchimedeanClass.mk_sub_lt_mk_left_iff, ArchimedeanClass.mk_map_of_archimedean', FiniteArchimedeanClass.addSubgroup_eq_bot, HahnEmbedding.Partial.exists_isMax, ArchimedeanClass.ball_antitone, HahnEmbedding.Seed.domain_baseEmbedding, ArchimedeanClass.mem_closedBallAddSubgroup_iff, FiniteArchimedeanClass.withTopOrderIso_apply_coe, ArchimedeanClass.mk_inv, FiniteArchimedeanClass.mem_closedBall_iff, ArchimedeanClass.FiniteElement.ext_iff, ArchimedeanClass.closedBall_top, hahnEmbedding_isOrderedAddMonoid, ArchimedeanClass.orderHom_injective, Hyperreal.archimedeanClassMk_epsilon_pos, Hyperreal.tendsto_atTop_iff, hahnEmbedding_isOrderedModule, ArchimedeanClass.mk_zpow, HahnEmbedding.Partial.toOrderAddMonoidHom_injective
ArchimedeanOrder πŸ“–CompOp
9 mathmath: ArchimedeanOrder.le_def, ArchimedeanOrder.instNonempty, ArchimedeanOrder.val_of, ArchimedeanOrder.of_val, ArchimedeanOrder.val_symm_eq, ArchimedeanOrder.lt_def, ArchimedeanOrder.of_symm_eq, ArchimedeanOrder.instTotalLe, ArchimedeanOrder.instSubsingleton
FiniteArchimedeanClass πŸ“–CompOp
49 mathmath: HahnEmbedding.IsPartial.baseEmbedding_le, FiniteArchimedeanClass.mem_addSubgroup_iff, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, FiniteArchimedeanClass.mk_lt_mk, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, HahnEmbedding.Seed.baseEmbedding_strictMono, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, HahnEmbedding.Partial.isWF_support_evalCoeff, HahnEmbedding.Partial.orderTop_eq_iff, FiniteArchimedeanClass.instSubsingletonOfAddArchimedean, HahnEmbedding.IsPartial.strictMono, FiniteArchimedeanClass.liftOrderHom_mk, HahnEmbedding.IsPartial.truncLT_mem_range, FiniteArchimedeanClass.instNonemptyOfNontrivial, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, FiniteArchimedeanClass.mem_ball_iff, HahnEmbedding.Partial.eval_smul, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, FiniteArchimedeanClass.mk_le_mk, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, HahnEmbedding.ArchimedeanStrata.iSupIndep_stratum', hahnEmbedding_isOrderedModule_rat, FiniteArchimedeanClass.congrOrderIso_symm, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, FiniteArchimedeanClass.withTopOrderIso_symm_apply, HahnEmbedding.Partial.mem_domain, HahnEmbedding.Seed.mem_domain_baseEmbedding, FiniteArchimedeanClass.addSubgroup_strictAnti, FiniteArchimedeanClass.coe_congrOrderIso_apply, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, FiniteArchimedeanClass.submodule_strictAnti, FiniteArchimedeanClass.ball_strictAnti, HahnEmbedding.Partial.eval_zero, HahnSeries.finiteArchimedeanClassOrderIso_apply, FiniteArchimedeanClass.min_le_mk_add, HahnEmbedding.Partial.exists_domain_eq_top, FiniteArchimedeanClass.addSubgroup_eq_bot, HahnEmbedding.Partial.exists_isMax, HahnEmbedding.Seed.domain_baseEmbedding, FiniteArchimedeanClass.withTopOrderIso_apply_coe, HahnEmbedding.ArchimedeanStrata.iSupIndep_stratum, FiniteArchimedeanClass.mem_closedBall_iff, hahnEmbedding_isOrderedAddMonoid, hahnEmbedding_isOrderedModule, HahnEmbedding.Partial.toOrderAddMonoidHom_injective
FiniteMulArchimedeanClass πŸ“–CompOp
17 mathmath: FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, FiniteMulArchimedeanClass.liftOrderHom_mk, FiniteMulArchimedeanClass.mk_le_mk, FiniteMulArchimedeanClass.mem_subgroup_iff, FiniteMulArchimedeanClass.congrOrderIso_symm, FiniteMulArchimedeanClass.min_le_mk_mul, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, FiniteMulArchimedeanClass.subgroup_eq_bot, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, FiniteMulArchimedeanClass.mk_lt_mk, FiniteMulArchimedeanClass.instSubsingletonOfMulArchimedean, FiniteMulArchimedeanClass.subgroup_strictAnti, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, FiniteMulArchimedeanClass.instNonemptyOfNontrivial
MulArchimedeanClass πŸ“–CompOp
55 mathmath: MulArchimedeanClass.subgroup_strictAntiOn, MulArchimedeanClass.orderHom_injective, MulArchimedeanClass.range_mk, MulArchimedeanClass.top_eq_mk_iff, MulArchimedeanClass.mk_left_le_mk_mul_iff, MulArchimedeanClass.mem_subgroup_iff, MulArchimedeanClass.subsemigroup_strictAnti, MulArchimedeanClass.mk_lt_mk, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, MulArchimedeanClass.liftOrderHom_mk, MulArchimedeanClass.min_le_mk_mul, MulArchimedeanClass.mem_closedBallSubgroup_iff, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, MulArchimedeanClass.mk_mul_lt_mk_left_iff, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, MulArchimedeanClass.mk_le_mk_iff_lt, FiniteMulArchimedeanClass.liftOrderHom_mk, MulArchimedeanClass.mk_antitoneOn, MulArchimedeanClass.mk_monotoneOn, MulArchimedeanClass.ballSubgroup_antitone, MulArchimedeanClass.mk_div_lt_mk_left_iff, MulArchimedeanClass.instNontrivial, MulArchimedeanClass.mk_right_le_mk_mul_iff, MulArchimedeanClass.mk_one, FiniteMulArchimedeanClass.mk_le_mk, FiniteMulArchimedeanClass.mem_subgroup_iff, FiniteMulArchimedeanClass.congrOrderIso_symm, FiniteMulArchimedeanClass.min_le_mk_mul, MulArchimedeanClass.mk_mul_lt_mk_right_iff, MulArchimedeanClass.out_top, MulArchimedeanClass.mk_left_le_mk_div_iff, MulArchimedeanClass.ballSubgroup_top, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, MulArchimedeanClass.mem_ballSubgroup_iff, FiniteMulArchimedeanClass.subgroup_eq_bot, MulArchimedeanClass.subgroup_antitone, MulArchimedeanClass.closedBallSubgroup_top, MulArchimedeanClass.mk_le_mk, MulArchimedeanClass.mk_eq_top_iff, MulArchimedeanClass.mk_le_mk_of_mabs, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, MulArchimedeanClass.mk_surjective, FiniteMulArchimedeanClass.val_mk, FiniteMulArchimedeanClass.mk_lt_mk, MulArchimedeanClass.mk_right_le_mk_div_iff, MulArchimedeanClass.orderHom_mk, MulArchimedeanClass.min_le_mk_div, FiniteMulArchimedeanClass.subgroup_strictAnti, MulArchimedeanClass.subgroup_eq_bot, MulArchimedeanClass.mk_div_lt_mk_right_iff, MulArchimedeanClass.min_le_mk_of_le_of_le, MulArchimedeanClass.instSubsingleton, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, MulArchimedeanClass.orderHom_top
MulArchimedeanOrder πŸ“–CompOp
9 mathmath: MulArchimedeanOrder.val_symm_eq, MulArchimedeanOrder.instNonempty, MulArchimedeanOrder.of_symm_eq, MulArchimedeanOrder.instTotalLe, MulArchimedeanOrder.lt_def, MulArchimedeanOrder.instSubsingleton, MulArchimedeanOrder.of_val, MulArchimedeanOrder.le_def, MulArchimedeanOrder.val_of

---

← Back to Index