Documentation Verification Report

Basic

📁 Source: Mathlib/Order/Filter/Basic.lean

Statistics

MetricCount
DefinitionsGenerateSets, generate, giGenerate, inhabitedMem, instCoframe, instCompleteLatticeFilter, instDistribLattice, instInhabited, instTransForallEventuallyEq, instTransForallEventuallyEqEventuallyLE, instTransForallEventuallyLE, instTransForallEventuallyLEEventuallyEq, instTransSetMemSubset, instTransSetSupersetMem, mkOfClosure, unique
16
TheoremseventuallyEq, and, and_frequently, choice, exists, exists_mem, filter_mono, forall_mem, frequently, lt_top_iff_ne_top, lt_top_of_ne, mono, mp, ne_of_lt, ne_top_of_lt, of_forall, set_eq, add, add_left, add_right, compl, comp₂, congr_left, congr_right, const_smul, const_vadd, diff, div, eventually, exists_mem, filter_mono, fun_add, fun_comp, fun_const_smul, fun_const_vadd, fun_div, fun_inv, fun_mul, fun_neg, fun_pow_const, fun_star, fun_sub, inf, inter, inv, le, mem_iff, mul, mul_left, mul_right, neg, of_eq, pow_const, preimage, prodMk, refl, rfl, rw, smul, sub, sub_eq, sup, symmDiff, trans, trans_le, union, vadd, antisymm, compl, diff, ge_iff_eq', inter, le_sup_of_le_left, le_sup_of_le_right, refl, rfl, sup, sup_le, trans, trans_eq, union, and_eventually, exists, filter_mono, inf_principal, mono, mp, of_forall, of_inf_principal, Iic_principal, mono, ne, nonempty, nonempty_of_mem, not_disjoint, biInf_sets_eq, biInter_mem', bot_sets_eq, coext, compl_mem_comk, compl_notMem, congr_sets, copy_eq, diff_mem, diff_mem_inf_principal_compl, disjoint_iff, disjoint_of_disjoint_of_mem, empty_mem_iff_bot, empty_notMem, eq_biInf_of_mem_iff_exists_mem, eq_iInf_of_mem_iff_exists_mem, eq_or_neBot, eq_sInf_of_mem_iff_exists_mem, eq_top_of_neBot, eventuallyEq_comm, eventuallyEq_empty, eventuallyEq_iff_all_subsets, eventuallyEq_iff_exists_mem, eventuallyEq_iff_sub, eventuallyEq_inf_principal_iff, eventuallyEq_of_mem, eventuallyEq_principal, eventuallyEq_set, eventuallyEq_top, eventuallyEq_univ, eventuallyLE_antisymm_iff, eventuallyLE_congr, eventuallyLE_iff_all_subsets, eventually_and, eventually_bot, eventually_congr, eventually_const, eventually_false_iff_eq_bot, eventually_iSup, eventually_iff, eventually_iff_all_subsets, eventually_iff_exists_mem, eventually_imp_distrib_left, eventually_imp_distrib_right, eventually_inf, eventually_inf_principal, eventually_mem_principal, eventually_mem_set, eventually_of_mem, eventually_or_distrib_left, eventually_or_distrib_right, eventually_principal, eventually_sSup, eventually_sup, eventually_top, eventually_true, exists_mem_and_iff, exists_mem_subset_iff, ext', filter_eq_bot_of_isEmpty, filter_eq_iff, forall_eventually_of_eventually_forall, forall_mem_nonempty_iff_neBot, frequently_and_distrib_left, frequently_and_distrib_right, frequently_bot, frequently_congr, frequently_const, frequently_false, frequently_iSup, frequently_iff, frequently_iff_forall_eventually_exists_and, frequently_iff_neBot, frequently_imp_distrib, frequently_imp_distrib_left, frequently_imp_distrib_right, frequently_inf_principal, frequently_mem_iff_neBot, frequently_or_distrib, frequently_or_distrib_left, frequently_or_distrib_right, frequently_principal, frequently_sSup, frequently_sup, frequently_top, frequently_true_iff_neBot, generate_empty, generate_eq_biInf, generate_iUnion, generate_singleton, generate_union, generate_univ, iInf_eq_generate, iInf_neBot_iff_of_directed, iInf_neBot_iff_of_directed', iInf_neBot_of_directed, iInf_neBot_of_directed', iInf_sets_eq, iInf_sets_induct, iInter_mem', iSup_inf_principal, iSup_join, iSup_neBot, iSup_principal, iSup_sets_eq, inf_eq_bot_iff, inf_principal, inf_principal_eq_bot, instNeBotTop, instNontrivialFilter, inter_eventuallyEq_left, inter_eventuallyEq_right, inter_mem_iff, inter_mem_inf, isCompl_principal, join_le, join_mono, join_principal_eq_sSup, le_generate_iff, le_principal_iff, mem_biInf_of_directed, mem_generate_of_mem, mem_iInf_of_directed, mem_iInf_of_mem, mem_iSup, mem_inf_iff, mem_inf_iff_superset, mem_inf_of_inter, mem_inf_of_left, mem_inf_of_right, mem_inf_principal, mem_inf_principal', mem_of_eq_bot, mem_principal_self, mem_sdiff_iff_union, mem_sup, mkOfClosure_sets, monotone_mem, monotone_principal, neBot_of_le, nonempty_of_mem, nonempty_of_neBot, nontrivial_iff_nonempty, not_disjoint_self_iff, not_eventually, not_frequently, not_le, not_neBot, principal_empty, principal_eq_bot_iff, principal_eq_iff_eq, principal_le_iff, principal_mono, principal_neBot_iff, principal_univ, sInf_neBot_of_directed, sInf_neBot_of_directed', sSup_sets_eq, set_eventuallyEq_iff_inf_principal, set_eventuallyLE_iff_inf_principal_le, set_eventuallyLE_iff_mem_inf_principal, sets_ssubset_sets, sets_subset_sets, skolem, sup_join, sup_neBot, sup_principal, sup_sets_eq, union_mem_sup, eventuallyLE, eventuallyEq, eventuallyEq_of_mem, principal_neBot
268
Total284

Eq

Theorems

NameKindAssumesProvesValidatesDepends On
eventuallyEq 📖mathematicalFilter.EventuallyEqFilter.EventuallyEq.of_eq

Filter

Definitions

NameCategoryTheorems
GenerateSets 📖CompData
generate 📖CompOp
27 mathmath: smallSets_eq_generate, HasBasis.eq_generate, IsBasis.filter_eq_generate, generate_singleton, atTop_eq_generate_Ici, le_generate_iff, map_generate_le_generate_preimage_preimage, mem_generate_of_mem, generate_union, generate_image_preimage_le_comap, hasBasis_generate, IsCountablyGenerated.out, ofSets_filter_eq_generate, generate_eq_biInf, atBot_eq_generate_of_forall_exists_le, mem_generate_iff, generate_neBot_iff, generate_empty, generate_eq_generate_inter, atTop_eq_generate_of_forall_exists_le, FilterBasis.generate, atBot_eq_generate_Iic, generate_univ, generate_iUnion, iInf_eq_generate, atBot_eq_generate_of_not_bddBelow, atTop_eq_generate_of_not_bddAbove
giGenerate 📖CompOp
inhabitedMem 📖CompOp
instCoframe 📖CompOp
1 mathmath: RestrictedProduct.isEmbedding_inclusion_top
instCompleteLatticeFilter 📖CompOp
95 mathmath: SeminormedGroup.disjoint_nhds, MeasureTheory.Measure.mutuallySingular_tfae, disjoint_comap_iff, disjoint_cocompact_left, disjoint_nhds_cocompact, t1Space_iff_disjoint_nhds_pure, disjoint_principal_left, isSeparatedMap_iff_disjoint_nhds, disjoint_comap_iff_map', T25Space.t2_5, Metric.disjoint_cobounded_nhdsSet, HasBasis.disjoint_iff_right, Metric.disjoint_nhds_cobounded, disjoint_atTop_principal_Iio, isOpen_setOf_disjoint_nhds_nhds, disjoint_nhds_nhds_iff_not_specializes, mem_codiscrete, SeparatedNhds.disjoint_nhdsSet, disjoint_nhdsSet_principal, Disjoint.filter_principal, disjoint_iff, SeminormedAddGroup.disjoint_nhds_zero, not_nonneg_sub_iff, isClosed_and_discrete_iff, r1Space_iff_inseparable_or_disjoint_nhds, isAtom_pure, disjoint_atBot_atTop, disjoint_cofinite_right, IsLindelof.disjoint_nhdsSet_left, disjoint_map, disjoint_cofinite_left, IsCompact.disjoint_nhdsSet_left, IsLindelof.disjoint_nhdsSet_right, not_disjoint_self_iff, disjoint_of_disjoint_of_mem, separatedNhds_iff_disjoint, disjoint_nhdsSet_nhdsSet, nonneg_sub_iff, disjoint_nhds_atBot_iff, Real.disjoint_residual_ae, clusterPt_iff_not_disjoint, HasBasis.disjoint_iff, t2Space_iff_disjoint_nhds, CompletelyNormalSpace.completely_normal, MeasureTheory.Measure.mutuallySingular_iff_disjoint_ae, disjoint_principal_principal, RegularSpace.regular, Set.pairwiseDisjoint_nhds, disjoint_comap_iff_map, disjoint_pure_pure, R1Space.specializes_or_disjoint_nhds, disjoint_nhds_nhds_iff_not_inseparable, disjoint_nhds_nhdsSet, not_one_le_div_iff, t1Space_iff_disjoint_pure_nhds, mem_codiscreteWithin, disjoint_pure_nhds, disjoint_atTop_principal_Iic, disjoint_nhds_atTop, Metric.disjoint_cobounded_nhds, HasBasis.disjoint_iff_left, disjoint_principal_nhdsSet, regularSpace_generateFrom, one_le_div_iff, disjoint_atTop_atBot, SeminormedGroup.disjoint_nhds_one, disjoint_prod, regularSpace_iff, disjoint_atBot_principal_Ioi, instIsAtomicFilter, specializes_iff_not_disjoint, MeasureTheory.Measure.MutuallySingular.disjoint_ae, disjoint_nhds_pure, disjoint_lift'_closure_nhds, disjoint_cocompact_right, disjoint_pure_atBot, r1Space_iff_specializes_or_disjoint_nhds, compl_diagonal_mem_prod, pairwise_disjoint_nhds, disjoint_nhds_atTop_iff, IsCompact.disjoint_nhdsSet_right, HasBasis.disjoint_cobounded_iff, disjoint_atBot_principal_Ici, Metric.disjoint_nhdsSet_cobounded, disjoint_nhdsSet_nhds, disjoint_pure_atTop, SeminormedAddGroup.disjoint_nhds, IsCompact.disjoint_nhdsSet_nhds, Specializes.not_disjoint, isCompl_principal, disjoint_nhds_atBot, Ultrafilter.isAtom, disjoint_nhds_nhds, disjoint_principal_right, Ultrafilter.disjoint_iff_not_le
instDistribLattice 📖CompOp
instInhabited 📖CompOp
instTransForallEventuallyEq 📖CompOp
instTransForallEventuallyEqEventuallyLE 📖CompOp
instTransForallEventuallyLE 📖CompOp
instTransForallEventuallyLEEventuallyEq 📖CompOp
instTransSetMemSubset 📖CompOp
instTransSetSupersetMem 📖CompOp
mkOfClosure 📖CompOp
1 mathmath: mkOfClosure_sets
unique 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
Iic_principal 📖mathematicalSet.Iic
Filter
PartialOrder.toPreorder
instPartialOrder
principal
setOf
Set
instMembership
Set.ext
le_principal_iff
biInf_sets_eq 📖mathematicalDirectedOn
Order.Preimage
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Set.Nonempty
sets
iInf
instInfSet
Set
Set.instMembership
Set.iUnion
Set.ext
mem_biInf_of_directed
biInter_mem' 📖mathematicalSet.SubsingletonSet
Filter
instMembership
Set.iInter
Set.instMembership
Set.Subsingleton.induction_on
Set.iInter_congr_Prop
Set.iInter_of_empty
instIsEmptyFalse
Set.iInter_univ
Set.iInter_iInter_eq_left
bot_sets_eq 📖mathematicalsets
Bot.bot
Filter
instBot
Set.univ
Set
coext 📖Set
Filter
instMembership
Compl.compl
Set.instCompl
ext
Function.Surjective.forall
compl_surjective
compl_mem_comk 📖mathematicalSet
Set.instEmptyCollection
Set.instUnion
Filter
instMembership
Compl.compl
Set.instCompl
compl_compl
compl_notMem 📖mathematicalSet
Filter
instMembership
Compl.compl
Set.instCompl
Set.Nonempty.ne_empty
nonempty_of_mem
inter_mem
Set.inter_compl_self
congr_sets 📖Set
Filter
instMembership
setOf
Set.instMembership
mp_mem
mem_of_superset
copy_eq 📖mathematicalSet
Set.instMembership
Filter
instMembership
copyext
diff_mem 📖mathematicalSet
Filter
instMembership
Compl.compl
Set.instCompl
Set.instSDiffinter_mem
diff_mem_inf_principal_compl 📖mathematicalSet
Filter
instMembership
instInf
principal
Compl.compl
Set.instCompl
Set.instSDiff
inter_mem_inf
mem_principal_self
disjoint_iff 📖mathematicalDisjoint
Filter
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLatticeFilter
Set
instMembership
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
disjoint_of_disjoint_of_mem 📖mathematicalDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Filter
instMembership
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLatticeFilter
disjoint_iff
empty_mem_iff_bot 📖mathematicalSet
Filter
instMembership
Set.instEmptyCollection
Bot.bot
instBot
bot_unique
mem_of_superset
Set.empty_subset
mem_bot
empty_notMem 📖mathematicalSet
Filter
instMembership
Set.instEmptyCollection
Set.Nonempty.ne_empty
nonempty_of_mem
eq_biInf_of_mem_iff_exists_mem 📖mathematicalSet
Filter
instMembership
iInf
instInfSet
iInf_subtype'
eq_iInf_of_mem_iff_exists_mem
eq_iInf_of_mem_iff_exists_mem 📖mathematicalSet
Filter
instMembership
iInf
instInfSet
eq_sInf_of_mem_iff_exists_mem
Set.exists_range_iff
eq_or_neBot 📖mathematicalBot.bot
Filter
instBot
NeBot
eq_or_ne
eq_sInf_of_mem_iff_exists_mem 📖mathematicalSet
Filter
instMembership
Set.instMembership
InfSet.sInf
instInfSet
le_antisymm
le_sInf
sInf_le
eq_top_of_neBot 📖mathematicalTop.top
Filter
instTop
top_unique
univ_mem
Subsingleton.eq_univ_of_nonempty
nonempty_of_mem
eventuallyEq_comm 📖mathematicalEventuallyEqEventuallyEq.symm
eventuallyEq_empty 📖mathematicalEventuallyEq
Set
Set.instEmptyCollection
Eventually
Set.instMembership
eventuallyEq_set
eventuallyEq_iff_all_subsets 📖mathematicalEventuallyEq
Eventually
eventually_iff_all_subsets
eventuallyEq_iff_exists_mem 📖mathematicalEventuallyEq
Set
Filter
instMembership
Set.EqOn
eventually_iff_exists_mem
eventuallyEq_iff_sub 📖mathematicalEventuallyEq
Pi.instSub
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
Pi.instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
EventuallyEq.sub_eq
sub_add_cancel
zero_add
EventuallyEq.add
EventuallyEq.refl
eventuallyEq_inf_principal_iff 📖mathematicalEventuallyEq
Filter
instInf
principal
Eventually
eventually_inf_principal
eventuallyEq_of_mem 📖mathematicalSet
Filter
instMembership
Set.EqOn
EventuallyEqeventually_of_mem
eventuallyEq_principal 📖mathematicalEventuallyEq
principal
Set.EqOn
eventuallyEq_set 📖mathematicalEventuallyEq
Eventually
Set
Set.instMembership
eventually_congr
Eventually.of_forall
eventuallyEq_top 📖mathematicalEventuallyEq
Top.top
Filter
instTop
eventuallyEq_univ 📖mathematicalEventuallyEq
Set.univ
Set
Filter
instMembership
eventuallyLE_antisymm_iff 📖mathematicalEventuallyEq
EventuallyLE
Preorder.toLE
PartialOrder.toPreorder
eventuallyLE_congr 📖mathematicalEventuallyEqEventuallyLEEventuallyLE.congr
EventuallyEq.symm
eventuallyLE_iff_all_subsets 📖mathematicalEventuallyLE
Eventually
eventually_iff_all_subsets
eventually_and 📖mathematicalEventuallyinter_mem_iff
eventually_bot 📖mathematicalEventually
Bot.bot
Filter
instBot
eventually_congr 📖EventuallyEventually.congr
eventually_const 📖mathematicalEventuallyNeBot.ne
eventually_false_iff_eq_bot 📖mathematicalEventually
Bot.bot
Filter
instBot
empty_mem_iff_bot
eventually_iSup 📖mathematicalEventually
iSup
Filter
instSupSet
mem_iSup
eventually_iff 📖mathematicalEventually
Set
Filter
instMembership
setOf
eventually_iff_all_subsets 📖mathematicalEventuallymp_mem
univ_mem'
eventually_iff_exists_mem 📖mathematicalEventually
Set
Filter
instMembership
exists_mem_subset_iff
eventually_imp_distrib_left 📖mathematicalEventually
eventually_imp_distrib_right 📖mathematicalEventually
eventually_inf 📖mathematicalEventually
Filter
instInf
Set
instMembership
mem_inf_iff_superset
eventually_inf_principal 📖mathematicalEventually
Filter
instInf
principal
mem_inf_principal
eventually_mem_principal 📖mathematicalEventually
Set
Set.instMembership
principal
mem_principal_self
eventually_mem_set 📖mathematicalEventually
Set
Set.instMembership
Filter
instMembership
eventually_of_mem 📖mathematicalSet
Filter
instMembership
Eventuallymem_of_superset
eventually_or_distrib_left 📖mathematicalEventuallyby_cases
eventually_or_distrib_right 📖mathematicalEventually
eventually_principal 📖mathematicalEventually
principal
eventually_sSup 📖mathematicalEventually
SupSet.sSup
Filter
instSupSet
eventually_sup 📖mathematicalEventually
Filter
instSup
eventually_top 📖mathematicalEventually
Top.top
Filter
instTop
eventually_true 📖mathematicalEventuallyuniv_mem
exists_mem_and_iff 📖mathematicalAntitone
Set
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Prop.partialOrder
Filter
instMembership
inter_mem
Set.inter_subset_left
Set.inter_subset_right
exists_mem_subset_iff 📖mathematicalSet
Filter
instMembership
Set.instHasSubset
mem_of_superset
Set.Subset.rfl
ext' 📖Eventuallyext
filter_eq_bot_of_isEmpty 📖mathematicalBot.bot
Filter
instBot
empty_mem_iff_bot
univ_mem'
filter_eq_iff 📖mathematicalsetsfilter_eq
forall_eventually_of_eventually_forall 📖EventuallyEventually.mono
forall_mem_nonempty_iff_neBot 📖mathematicalSet.Nonempty
NeBot
Set.not_nonempty_empty
mem_bot
nonempty_of_mem
frequently_and_distrib_left 📖mathematicalFrequently
frequently_and_distrib_right 📖mathematicalFrequently
frequently_bot 📖mathematicalFrequently
Bot.bot
Filter
instBot
frequently_congr 📖mathematicalEventuallyFrequentlyFrequently.mp
Eventually.mono
frequently_const 📖mathematicalFrequently
frequently_false 📖mathematicalFrequently
frequently_iSup 📖mathematicalFrequently
iSup
Filter
instSupSet
frequently_iff 📖mathematicalFrequently
Set
Set.instMembership
frequently_iff_forall_eventually_exists_and 📖mathematicalFrequentlyFrequently.exists
Frequently.and_eventually
frequently_iff_neBot 📖mathematicalFrequently
NeBot
Filter
instInf
principal
setOf
neBot_iff
inf_principal_eq_bot
frequently_imp_distrib 📖mathematicalFrequently
frequently_imp_distrib_left 📖mathematicalFrequently
frequently_imp_distrib_right 📖mathematicalFrequently
frequently_inf_principal 📖mathematicalFrequently
Filter
instInf
principal
Set
Set.instMembership
frequently_mem_iff_neBot 📖mathematicalFrequently
Set
Set.instMembership
NeBot
Filter
instInf
principal
frequently_iff_neBot
frequently_or_distrib 📖mathematicalFrequently
frequently_or_distrib_left 📖mathematicalFrequently
frequently_or_distrib_right 📖mathematicalFrequently
frequently_principal 📖mathematicalFrequently
principal
Set
Set.instMembership
frequently_sSup 📖mathematicalFrequently
SupSet.sSup
Filter
instSupSet
Set
Set.instMembership
frequently_sup 📖mathematicalFrequently
Filter
instSup
frequently_top 📖mathematicalFrequently
Top.top
Filter
instTop
frequently_true_iff_neBot 📖mathematicalFrequently
NeBot
principal_univ
inf_of_le_left
generate_empty 📖mathematicalgenerate
Set
Set.instEmptyCollection
Top.top
Filter
instTop
GaloisConnection.l_bot
GaloisInsertion.gc
generate_eq_biInf 📖mathematicalgenerate
iInf
Filter
Set
instInfSet
Set.instMembership
principal
eq_of_forall_le_iff
generate_iUnion 📖mathematicalgenerate
Set.iUnion
Set
iInf
Filter
instInfSet
GaloisConnection.l_iSup
GaloisInsertion.gc
generate_singleton 📖mathematicalgenerate
Set
Set.instSingletonSet
principal
le_antisymm
mem_of_superset
mem_generate_of_mem
Set.mem_singleton
le_generate_iff
Set.singleton_subset_iff
Set.Subset.rfl
generate_union 📖mathematicalgenerate
Set
Set.instUnion
Filter
instInf
GaloisConnection.l_sup
GaloisInsertion.gc
generate_univ 📖mathematicalgenerate
Set.univ
Set
Bot.bot
Filter
instBot
bot_unique
Set.mem_univ
iInf_eq_generate 📖mathematicaliInf
Filter
instInfSet
generate
Set.iUnion
Set
sets
eq_of_forall_le_iff
iInf_neBot_iff_of_directed 📖mathematicalDirected
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
NeBot
iInf
instInfSet
NeBot.mono
iInf_le
iInf_neBot_of_directed
iInf_neBot_iff_of_directed' 📖mathematicalDirected
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
NeBot
iInf
instInfSet
NeBot.mono
iInf_le
iInf_neBot_of_directed'
iInf_neBot_of_directed 📖mathematicalDirected
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
NeBot
iInf
instInfSet
isEmpty_or_nonempty
iInf_of_empty
instNontrivialFilter
iInf_neBot_of_directed'
iInf_neBot_of_directed' 📖mathematicalDirected
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
NeBot
iInf
instInfSet
not_imp_not
mem_iInf_of_directed
iInf_sets_eq 📖mathematicalDirected
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
sets
iInf
instInfSet
Set.iUnion
Set
Set.mem_iUnion
univ_mem
mem_of_superset
inter_mem
eq_iInf_of_mem_iff_exists_mem
iInf_sets_induct 📖Set
Filter
instMembership
iInf
instInfSet
Set.univ
Set.instInter
Set.inter_univ
mem_of_superset
LE.le.trans
inter_mem
mem_iInf_of_mem
Set.union_inter_distrib_left
Set.union_eq_left
Set.subset_union_right
Set.univ_inter
Set.inter_subset_inter_left
Set.inter_assoc
le_iInf_iff
HasSubset.Subset.trans
Set.instIsTransSubset
subset_rfl
Set.instReflSubset
iInter_mem' 📖mathematicalSet
Filter
instMembership
Set.iInter
Set.sInter_range
Set.sInter_eq_biInter
biInter_mem'
Set.subsingleton_range
Set.forall_mem_range
iSup_inf_principal 📖mathematicaliSup
Filter
instSupSet
instInf
principal
ext
iSup_join 📖mathematicaliSup
Filter
instSupSet
join
ext
iSup_neBot 📖mathematicalNeBot
iSup
Filter
instSupSet
iSup_principal 📖mathematicaliSup
Filter
instSupSet
principal
Set.iUnion
ext
iSup_sets_eq 📖mathematicalsets
iSup
Filter
instSupSet
Set.iInter
Set
GaloisConnection.u_iInf
GaloisInsertion.gc
inf_eq_bot_iff 📖mathematicalFilter
instInf
Bot.bot
instBot
Set
instMembership
Set.instInter
Set.instEmptyCollection
inf_principal 📖mathematicalFilter
instInf
principal
Set
Set.instInter
le_antisymm
Set.Subset.rfl
inf_principal_eq_bot 📖mathematicalFilter
instInf
principal
Bot.bot
instBot
Set
instMembership
Compl.compl
Set.instCompl
empty_mem_iff_bot
mem_inf_principal
instNeBotTop 📖mathematicalNeBot
Top.top
Filter
instTop
forall_mem_nonempty_iff_neBot
mem_top
Set.nonempty_iff_univ_nonempty
instNontrivialFilter 📖mathematicalNontrivial
Filter
NeBot.ne
instNeBotTop
inter_eventuallyEq_left 📖mathematicalEventuallyEq
Set
Set.instInter
Eventually
inter_eventuallyEq_right 📖mathematicalEventuallyEq
Set
Set.instInter
Eventually
Set.inter_comm
inter_eventuallyEq_left
inter_mem_iff 📖mathematicalSet
Filter
instMembership
Set.instInter
mem_of_superset
Set.inter_subset_left
Set.inter_subset_right
inter_mem
inter_mem_inf 📖mathematicalSet
Filter
instMembership
instInf
Set.instInter
isCompl_principal 📖mathematicalIsCompl
Filter
instPartialOrder
CompleteLattice.toBoundedOrder
instCompleteLatticeFilter
principal
Compl.compl
Set
Set.instCompl
IsCompl.of_eq
inf_principal
Set.inter_compl_self
principal_empty
sup_principal
Set.union_compl_self
principal_univ
join_le 📖mathematicalEventually
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
joinEventually.mono
join_mono 📖mathematicalFilter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
join
join_principal_eq_sSup 📖mathematicaljoin
principal
Filter
SupSet.sSup
instSupSet
le_generate_iff 📖mathematicalFilter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
generate
Set
Set.instHasSubset
sets
univ_mem
mem_of_superset
inter_mem
le_principal_iff 📖mathematicalFilter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
principal
Set
instMembership
Set.Subset.rfl
mem_of_superset
mem_biInf_of_directed 📖mathematicalDirectedOn
Order.Preimage
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Set.Nonempty
Set
instMembership
iInf
instInfSet
Set.instMembership
iInf_subtype'
mem_iInf_of_directed
DirectedOn.directed_val
Set.Nonempty.to_subtype
mem_generate_of_mem 📖mathematicalSet
Set.instMembership
Filter
instMembership
generate
mem_iInf_of_directed 📖mathematicalDirected
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Set
instMembership
iInf
instInfSet
iInf_sets_eq
mem_iInf_of_mem 📖mathematicalSet
Filter
instMembership
iInf
instInfSet
iInf_le
mem_iSup 📖mathematicalSet
Filter
instMembership
iSup
instSupSet
iSup_sets_eq
mem_inf_iff 📖mathematicalSet
Filter
instMembership
instInf
Set.instInter
mem_inf_iff_superset 📖mathematicalSet
Filter
instMembership
instInf
Set.instHasSubset
Set.instInter
Set.Subset.rfl
mem_inf_of_inter
mem_inf_of_inter 📖mathematicalSet
Filter
instMembership
Set.instHasSubset
Set.instInter
instInfmem_of_superset
inter_mem_inf
mem_inf_of_left 📖mathematicalSet
Filter
instMembership
instInfuniv_mem
Set.inter_univ
mem_inf_of_right 📖mathematicalSet
Filter
instMembership
instInfuniv_mem
Set.univ_inter
mem_inf_principal 📖mathematicalSet
Filter
instMembership
instInf
principal
setOf
mem_inf_principal' 📖mathematicalSet
Filter
instMembership
instInf
principal
Set.instUnion
Compl.compl
Set.instCompl
IsCompl.le_left_iff
isCompl_principal
inf_principal
IsCompl.le_right_iff
Set.compl_inter
compl_compl
mem_of_eq_bot 📖mathematicalFilter
instInf
principal
Compl.compl
Set
Set.instCompl
Bot.bot
instBot
instMembershipcompl_compl
inf_principal_eq_bot
mem_principal_self 📖mathematicalSet
Filter
instMembership
principal
Set.Subset.rfl
mem_sdiff_iff_union 📖mathematicalSet
Filter
instMembership
instSDiff
Set.instUnion
mem_of_superset
Set.subset_union_right
Set.subset_union_left
Set.union_eq_right
mem_sup 📖mathematicalSet
Filter
instMembership
instSup
mkOfClosure_sets 📖mathematicalsets
generate
mkOfClosureext
monotone_mem 📖mathematicalMonotone
Set
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Prop.partialOrder
Filter
instMembership
mem_of_superset
monotone_principal 📖mathematicalMonotone
Set
Filter
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
instPartialOrder
principal
principal_mono
neBot_of_le 📖mathematicalFilter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
NeBotNeBot.mono
nonempty_of_mem 📖mathematicalSet
Filter
instMembership
Set.NonemptySet.eq_empty_or_nonempty
empty_mem_iff_bot
NeBot.ne'
nonempty_of_neBot 📖nonempty_of_mem
univ_mem
nontrivial_iff_nonempty 📖mathematicalNontrivial
Filter
by_contra
not_subsingleton
Unique.instSubsingleton
not_nonempty_iff
instNontrivialFilter
not_disjoint_self_iff 📖mathematicalDisjoint
Filter
instPartialOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
instCompleteLatticeFilter
NeBot
disjoint_self
neBot_iff
not_eventually 📖mathematicalEventually
Frequently
not_frequently 📖mathematicalFrequently
Eventually
not_le 📖mathematicalFilter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Set
instMembership
not_neBot 📖mathematicalNeBot
Bot.bot
Filter
instBot
Iff.not_left
neBot_iff
principal_empty 📖mathematicalprincipal
Set
Set.instEmptyCollection
Bot.bot
Filter
instBot
bot_unique
Set.empty_subset
principal_eq_bot_iff 📖mathematicalprincipal
Bot.bot
Filter
instBot
Set
Set.instEmptyCollection
empty_mem_iff_bot
mem_principal
Set.subset_empty_iff
principal_eq_iff_eq 📖mathematicalprincipal
principal_le_iff 📖mathematicalFilter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
principal
Set
Set.instHasSubset
principal_mono 📖mathematicalFilter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
principal
Set
Set.instHasSubset
principal_neBot_iff 📖mathematicalNeBot
principal
Set.Nonempty
neBot_iff
principal_eq_bot_iff
Set.nonempty_iff_ne_empty
principal_univ 📖mathematicalprincipal
Set.univ
Top.top
Filter
instTop
top_unique
sInf_neBot_of_directed 📖mathematicalDirectedOn
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Set
Set.instMembership
Bot.bot
instBot
NeBot
InfSet.sInf
instInfSet
iInf_neBot_of_directed
DirectedOn.directed_val
sInf_eq_iInf'
sInf_neBot_of_directed' 📖mathematicalSet.Nonempty
Filter
DirectedOn
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Set
Set.instMembership
Bot.bot
instBot
NeBot
InfSet.sInf
instInfSet
iInf_neBot_of_directed'
Set.Nonempty.to_subtype
DirectedOn.directed_val
sInf_eq_iInf'
sSup_sets_eq 📖mathematicalsets
SupSet.sSup
Filter
instSupSet
Set.iInter
Set
Set.instMembership
GaloisConnection.u_sInf
GaloisInsertion.gc
set_eventuallyEq_iff_inf_principal 📖mathematicalEventuallyEq
Filter
instInf
principal
set_eventuallyLE_iff_inf_principal_le 📖mathematicalEventuallyLE
Prop.le
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instInf
principal
set_eventuallyLE_iff_mem_inf_principal
set_eventuallyLE_iff_mem_inf_principal 📖mathematicalEventuallyLE
Prop.le
Set
Filter
instMembership
instInf
principal
eventually_inf_principal
sets_ssubset_sets 📖mathematicalSet
Set.instHasSSubset
sets
Filter
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
sets_subset_sets 📖mathematicalSet
Set.instHasSubset
sets
Filter
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
skolem 📖mathematicalEventuallymp_mem
univ_mem'
Eventually.mp
Eventually.of_forall
sup_join 📖mathematicalFilter
instSup
join
ext
sup_neBot 📖mathematicalNeBot
Filter
instSup
sup_principal 📖mathematicalFilter
instSup
principal
Set
Set.instUnion
ext
sup_sets_eq 📖mathematicalsets
Filter
instSup
Set
Set.instInter
GaloisConnection.u_inf
GaloisInsertion.gc
union_mem_sup 📖mathematicalSet
Filter
instMembership
instSup
Set.instUnion
mem_of_superset
Set.subset_union_left
Set.subset_union_right

Filter.Eventually

Theorems

NameKindAssumesProvesValidatesDepends On
and 📖Filter.EventuallyFilter.inter_mem
and_frequently 📖Filter.Eventually
Filter.Frequently
Filter.Frequently.and_eventually
choice 📖Filter.Eventuallymono
exists
Function.sometimes_spec
exists 📖Filter.EventuallyFilter.Frequently.exists
frequently
exists_mem 📖mathematicalFilter.EventuallySet
Filter
Filter.instMembership
Filter.eventually_iff_exists_mem
filter_mono 📖Filter
Preorder.toLE
PartialOrder.toPreorder
Filter.instPartialOrder
Filter.Eventually
forall_mem 📖Filter.Eventually
Filter
Preorder.toLE
PartialOrder.toPreorder
Filter.instPartialOrder
Filter.principal
Set
Set.instMembership
Filter.eventually_principal
filter_mono
frequently 📖mathematicalFilter.EventuallyFilter.FrequentlyFilter.compl_notMem
lt_top_iff_ne_top 📖mathematicalFilter.Eventually
Preorder.toLT
PartialOrder.toPreorder
Top.top
OrderTop.toTop
Preorder.toLE
ne_of_lt
lt_top_of_ne
lt_top_of_ne 📖mathematicalFilter.Eventually
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLTmono
Ne.lt_top
mono 📖Filter.Eventuallymp
of_forall
mp 📖Filter.EventuallyFilter.mp_mem
ne_of_lt 📖Filter.Eventually
Preorder.toLT
mono
LT.lt.ne
ne_top_of_lt 📖mathematicalFilter.Eventually
Preorder.toLT
Top.top
OrderTop.toTop
Preorder.toLE
mono
LT.lt.ne_top
of_forall 📖mathematicalFilter.EventuallyFilter.univ_mem'
set_eq 📖mathematicalFilter.Eventually
Set
Set.instMembership
Filter.EventuallyEqFilter.eventuallyEq_set

Filter.EventuallyEq

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalFilter.EventuallyEqPi.instAddcomp₂
add_left 📖mathematicalFilter.EventuallyEqPi.instAddadd
refl
add_right 📖mathematicalFilter.EventuallyEqPi.instAddadd
refl
compl 📖mathematicalFilter.EventuallyEqCompl.compl
Set
Set.instCompl
fun_comp
comp₂ 📖Filter.EventuallyEqfun_comp
prodMk
congr_left 📖Filter.EventuallyEqtrans
symm
congr_right 📖Filter.EventuallyEqtrans
symm
const_smul 📖mathematicalFilter.EventuallyEqPi.instSMulfun_comp
const_vadd 📖mathematicalFilter.EventuallyEqHVAdd.hVAdd
instHVAdd
Pi.instVAdd
fun_comp
diff 📖mathematicalFilter.EventuallyEqSet
Set.instSDiff
inter
compl
div 📖mathematicalFilter.EventuallyEqPi.instDivcomp₂
eventually 📖mathematicalFilter.EventuallyEqFilter.Eventually
exists_mem 📖mathematicalFilter.EventuallyEqSet
Filter
Filter.instMembership
Set.EqOn
Filter.Eventually.exists_mem
filter_mono 📖Filter.EventuallyEq
Filter
Preorder.toLE
PartialOrder.toPreorder
Filter.instPartialOrder
fun_add 📖Filter.EventuallyEqadd
fun_comp 📖Filter.EventuallyEqFilter.Eventually.mono
fun_const_smul 📖Filter.EventuallyEqconst_smul
fun_const_vadd 📖mathematicalFilter.EventuallyEqHVAdd.hVAdd
instHVAdd
const_vadd
fun_div 📖Filter.EventuallyEqdiv
fun_inv 📖Filter.EventuallyEqinv
fun_mul 📖Filter.EventuallyEqmul
fun_neg 📖Filter.EventuallyEqneg
fun_pow_const 📖Filter.EventuallyEqpow_const
fun_star 📖mathematicalFilter.EventuallyEqStar.starfun_comp
fun_sub 📖Filter.EventuallyEqsub
inf 📖mathematicalFilter.EventuallyEqPi.instMinForall_mathlibcomp₂
inter 📖mathematicalFilter.EventuallyEqSet
Set.instInter
comp₂
inv 📖mathematicalFilter.EventuallyEqPi.instInvfun_comp
le 📖mathematicalFilter.EventuallyEqFilter.EventuallyLE
Preorder.toLE
Filter.Eventually.mono
le_of_eq
mem_iff 📖mathematicalFilter.EventuallyEqFilter.Eventually
Set
Set.instMembership
Filter.eventuallyEq_set
mul 📖mathematicalFilter.EventuallyEqPi.instMulcomp₂
mul_left 📖mathematicalFilter.EventuallyEqPi.instMulmul
refl
mul_right 📖mathematicalFilter.EventuallyEqPi.instMulmul
refl
neg 📖mathematicalFilter.EventuallyEqPi.instNegfun_comp
of_eq 📖mathematicalFilter.EventuallyEqrfl
pow_const 📖mathematicalFilter.EventuallyEqPi.instPowfun_comp
preimage 📖mathematicalFilter.EventuallyEqSet.preimagefun_comp
prodMk 📖Filter.EventuallyEqFilter.Eventually.mp
Filter.Eventually.mono
refl 📖mathematicalFilter.EventuallyEqFilter.Eventually.of_forall
rfl 📖mathematicalFilter.EventuallyEqrefl
rw 📖Filter.EventuallyEq
Filter.Eventually
Filter.Eventually.congr
Filter.Eventually.mono
smul 📖Filter.EventuallyEqcomp₂
sub 📖mathematicalFilter.EventuallyEqPi.instSubcomp₂
sub_eq 📖mathematicalFilter.EventuallyEqPi.instSub
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
Pi.instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
sub_self
symm
sub
refl
sup 📖mathematicalFilter.EventuallyEqPi.instMaxForall_mathlibcomp₂
symmDiff 📖mathematicalFilter.EventuallyEqsymmDiff
Set
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.instSDiff
union
diff
trans 📖Filter.EventuallyEqrw
trans_le 📖Filter.EventuallyEq
Filter.EventuallyLE
Preorder.toLE
Filter.EventuallyLE.trans
le
union 📖mathematicalFilter.EventuallyEqSet
Set.instUnion
comp₂
vadd 📖mathematicalFilter.EventuallyEqHVAdd.hVAdd
instHVAdd
comp₂

Filter.EventuallyLE

Theorems

NameKindAssumesProvesValidatesDepends On
antisymm 📖mathematicalFilter.EventuallyLE
Preorder.toLE
PartialOrder.toPreorder
Filter.EventuallyEqFilter.Eventually.mp
Filter.Eventually.mono
le_antisymm
compl 📖mathematicalFilter.EventuallyLE
Prop.le
Compl.compl
Set
Set.instCompl
Filter.Eventually.mono
diff 📖mathematicalFilter.EventuallyLE
Prop.le
Set
Set.instSDiff
inter
compl
ge_iff_eq' 📖mathematicalFilter.EventuallyLE
Preorder.toLE
PartialOrder.toPreorder
Filter.EventuallyEqantisymm
Filter.EventuallyEq.le
inter 📖mathematicalFilter.EventuallyLE
Prop.le
Set
Set.instInter
Filter.Eventually.mp
Filter.Eventually.mono
le_sup_of_le_left 📖mathematicalFilter.EventuallyLE
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Pi.instMaxForall_mathlib
SemilatticeSup.toMax
Filter.Eventually.mono
le_sup_of_le_left
le_sup_of_le_right 📖mathematicalFilter.EventuallyLE
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Pi.instMaxForall_mathlib
SemilatticeSup.toMax
Filter.Eventually.mono
le_sup_of_le_right
refl 📖mathematicalFilter.EventuallyLE
Preorder.toLE
Filter.EventuallyEq.le
Filter.EventuallyEq.rfl
rfl 📖mathematicalFilter.EventuallyLE
Preorder.toLE
refl
sup 📖mathematicalFilter.EventuallyLE
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Pi.instMaxForall_mathlib
SemilatticeSup.toMax
Filter.mp_mem
Filter.univ_mem'
sup_le_sup
sup_le 📖mathematicalFilter.EventuallyLE
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Pi.instMaxForall_mathlib
SemilatticeSup.toMax
Filter.mp_mem
Filter.univ_mem'
sup_le
trans 📖Filter.EventuallyLE
Preorder.toLE
Filter.Eventually.mp
Filter.Eventually.mono
le_trans
trans_eq 📖Filter.EventuallyLE
Preorder.toLE
Filter.EventuallyEq
trans
Filter.EventuallyEq.le
union 📖mathematicalFilter.EventuallyLE
Prop.le
Set
Set.instUnion
Filter.Eventually.mp
Filter.Eventually.mono

Filter.Frequently

Theorems

NameKindAssumesProvesValidatesDepends On
and_eventually 📖Filter.Frequently
Filter.Eventually
Filter.Eventually.mp
Filter.Eventually.mono
exists 📖Filter.FrequentlyFilter.Eventually.of_forall
filter_mono 📖Filter.Frequently
Filter
Preorder.toLE
PartialOrder.toPreorder
Filter.instPartialOrder
Filter.Eventually.filter_mono
inf_principal 📖mathematicalFilter.Frequently
Set
Set.instMembership
Filter
Filter.instInf
Filter.principal
Filter.frequently_inf_principal
mono 📖Filter.Frequentlymp
Filter.Eventually.of_forall
mp 📖Filter.Frequently
Filter.Eventually
Filter.Eventually.mp
Filter.Eventually.mono
of_forall 📖mathematicalFilter.FrequentlyFilter.Eventually.frequently
Filter.Eventually.of_forall
of_inf_principal 📖mathematicalFilter.Frequently
Filter
Filter.instInf
Filter.principal
Set
Set.instMembership
Filter.frequently_inf_principal

Filter.NeBot

Theorems

NameKindAssumesProvesValidatesDepends On
mono 📖mathematicalFilter
Preorder.toLE
PartialOrder.toPreorder
Filter.instPartialOrder
Filter.NeBotne_bot_of_le_ne_bot
ne'
ne 📖ne'
nonempty 📖not_isEmpty_iff
ne
Unique.instSubsingleton
nonempty_of_mem 📖mathematicalSet
Filter
Filter.instMembership
Set.NonemptyFilter.nonempty_of_mem
not_disjoint 📖mathematicalSet
Filter
Filter.instMembership
Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Filter.not_disjoint_self_iff
Filter.disjoint_iff

HasSubset.Subset

Theorems

NameKindAssumesProvesValidatesDepends On
eventuallyLE 📖mathematicalSet
Set.instHasSubset
Filter.EventuallyLE
Prop.le
Filter.Eventually.of_forall

Set.EqOn

Theorems

NameKindAssumesProvesValidatesDepends On
eventuallyEq 📖mathematicalSet.EqOnFilter.EventuallyEq
Filter.principal
eventuallyEq_of_mem 📖mathematicalSet.EqOn
Set
Filter
Filter.instMembership
Filter.EventuallyEqFilter.EventuallyEq.filter_mono
eventuallyEq
Filter.le_principal_iff

Set.Nonempty

Theorems

NameKindAssumesProvesValidatesDepends On
principal_neBot 📖mathematicalSet.NonemptyFilter.NeBot
Filter.principal
Filter.principal_neBot_iff

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