Documentation Verification Report

Basic

📁 Source: Mathlib/Order/Interval/Finset/Basic.lean

Statistics

MetricCount
DefinitionsIicFinsetSet, instUniqueSubtypeMemIicBot, fintypeOfMemBounds
3
Theoremsfinite, finite, nonempty_Icc_of_le, nonempty_Ico_of_lt, nonempty_Iio_of_not_isMin, nonempty_Ioc_of_lt, nonempty_Ioi_of_not_isMax, Icc_bot, Icc_bot_top, Icc_diff_Ico_self, Icc_diff_Ioc_self, Icc_diff_Ioo_self, Icc_diff_both, Icc_eq_cons_Ico, Icc_eq_cons_Ioc, Icc_eq_empty, Icc_eq_empty_iff, Icc_eq_empty_of_lt, Icc_eq_singleton_iff, Icc_erase_left, Icc_erase_right, Icc_filter_lt_of_lt_right, Icc_map_sectL, Icc_map_sectR, Icc_min_max, Icc_self, Icc_ssubset_Icc_left, Icc_ssubset_Icc_right, Icc_subset_Icc, Icc_subset_Icc_iff, Icc_subset_Icc_left, Icc_subset_Icc_right, Icc_subset_Ici_self, Icc_subset_Ico_iff, Icc_subset_Ico_right, Icc_subset_Iic_self, Icc_subset_Ioc_iff, Icc_subset_Ioo_iff, Icc_subset_uIcc, Icc_subset_uIcc', Icc_top, Ici_bot, Ici_eq_cons_Ioi, Ici_erase, Ici_ssubset_Ici, Ici_subset_Ici, Ici_top, Ico_bot, Ico_diff_Ico_left, Ico_diff_Ico_right, Ico_diff_Ioo_self, Ico_disjoint_Ico_consecutive, Ico_eq_cons_Ioo, Ico_eq_empty, Ico_eq_empty_iff, Ico_eq_empty_of_le, Ico_erase_left, Ico_filter_le, Ico_filter_le_left, Ico_filter_le_of_le_left, Ico_filter_le_of_left_le, Ico_filter_le_of_right_le, Ico_filter_lt, Ico_filter_lt_of_le_left, Ico_filter_lt_of_le_right, Ico_filter_lt_of_right_le, Ico_insert_right, Ico_inter_Ico, Ico_inter_Ico_consecutive, Ico_map_sectL, Ico_map_sectR, Ico_self, Ico_subset_Icc_self, Ico_subset_Ici_self, Ico_subset_Ico, Ico_subset_Ico_iff, Ico_subset_Ico_left, Ico_subset_Ico_right, Ico_subset_Ico_union_Ico, Ico_subset_Iic_self, Ico_subset_Iio_self, Ico_subset_Ioo_left, Ico_union_Ico, Ico_union_Ico', Ico_union_Ico_eq_Ico, Iic_bot, Iic_diff_Ioc, Iic_diff_Ioc_self_of_le, Iic_disjoint_Ioc, Iic_eq_cons_Iio, Iic_erase, Iic_filter_lt_of_lt_right, Iic_ssubset_Iic, Iic_subset_Iic, Iic_top, Iic_union_Ioc_eq_Iic, Iio_bot, Iio_eq_empty, Iio_filter_lt, Iio_insert, Iio_nonempty, Iio_ssubset_Iio, Iio_subset_Iic_self, Iio_subset_Iio, Ioc_diff_Ioo_self, Ioc_disjoint_Ioc, Ioc_disjoint_Ioc_of_le, Ioc_eq_cons_Ioo, Ioc_eq_empty, Ioc_eq_empty_iff, Ioc_eq_empty_of_le, Ioc_erase_right, Ioc_filter_lt_of_lt_right, Ioc_insert_left, Ioc_inter_Ioc, Ioc_map_sectL, Ioc_map_sectR, Ioc_self, Ioc_subset_Icc_self, Ioc_subset_Ici_self, Ioc_subset_Iic_self, Ioc_subset_Ioc, Ioc_subset_Ioc_left, Ioc_subset_Ioc_right, Ioc_subset_Ioi_self, Ioc_subset_Ioo_right, Ioc_top, Ioc_union_Ioc_eq_Ioc, Ioi_disjUnion_Iio, Ioi_eq_empty, Ioi_insert, Ioi_nonempty, Ioi_ssubset_Ioi, Ioi_subset_Ici_self, Ioi_subset_Ioi, Ioi_top, Ioo_eq_empty, Ioo_eq_empty_iff, Ioo_eq_empty_of_le, Ioo_filter_lt, Ioo_insert_left, Ioo_insert_right, Ioo_map_sectL, Ioo_map_sectR, Ioo_self, Ioo_subset_Icc_self, Ioo_subset_Ici_self, Ioo_subset_Ico_self, Ioo_subset_Iic_self, Ioo_subset_Iio_self, Ioo_subset_Ioc_self, Ioo_subset_Ioi_self, Ioo_subset_Ioo, Ioo_subset_Ioo_left, Ioo_subset_Ioo_right, card_Ico_eq_card_Icc_sub_one, card_Iio_eq_card_Iic_sub_one, card_Ioc_eq_card_Icc_sub_one, card_Ioi_eq_card_Ici_sub_one, card_Ioo_eq_card_Icc_sub_two, card_Ioo_eq_card_Ico_sub_one, card_Ioo_eq_card_Ioc_sub_one, disjoint_Ioi_Iio, eq_of_mem_uIcc_of_mem_uIcc, eq_of_mem_uIcc_of_mem_uIcc', filter_ge_eq_Iic, filter_gt_eq_Iio, filter_le_eq_Ici, filter_le_le_eq_Icc, filter_le_lt_eq_Ico, filter_lt_eq_Ioi, filter_lt_le_eq_Ioc, filter_lt_lt_eq_Ioo, image_subset_Iic_sup, inf'_Ici, inf_Ici, left_mem_Icc, left_mem_Ico, left_mem_uIcc, left_notMem_Ioc, left_notMem_Ioo, mem_uIcc', mem_uIcc_of_ge, mem_uIcc_of_le, nonempty_Icc, nonempty_Ici, nonempty_Ico, nonempty_Iic, nonempty_Iio, nonempty_Ioc, nonempty_Ioi, nonempty_Ioo, nonempty_uIcc, notMem_Iio_self, notMem_Ioi_self, notMem_uIcc_of_gt, notMem_uIcc_of_lt, right_mem_Icc, right_mem_Ioc, right_mem_uIcc, right_notMem_Ico, right_notMem_Ioo, subset_Iic_sup_id, sup'_Iic, sup_Iic, uIcc_comm, uIcc_eq_union, uIcc_injective_left, uIcc_injective_right, uIcc_map_sectL, uIcc_map_sectR, uIcc_of_ge, uIcc_of_le, uIcc_of_not_ge, uIcc_of_not_le, uIcc_self, uIcc_subset_Icc, uIcc_subset_uIcc, uIcc_subset_uIcc_iff_le, uIcc_subset_uIcc_iff_le', uIcc_subset_uIcc_iff_mem, uIcc_subset_uIcc_left, uIcc_subset_uIcc_right, uIcc_subset_uIcc_union_uIcc, uIcc_toDual, finsetIoi_eq, finsetIio_eq, exists_gt, exists_lt, not_bddAbove, not_bddBelow, infinite_iff_exists_gt, infinite_iff_exists_lt, antitone_iff_forall_covBy, antitone_iff_forall_wcovBy, le_iff_reflTransGen_covBy, le_iff_transGen_wcovBy, lt_iff_transGen_covBy, monotone_iff_forall_covBy, monotone_iff_forall_wcovBy, not_lt_of_denselyOrdered_of_locallyFinite, strictAnti_iff_forall_covBy, strictMono_iff_forall_covBy, transGen_covBy_of_lt, transGen_wcovBy_of_le
245
Total248

BddAbove

Theorems

NameKindAssumesProvesValidatesDepends On
finite 📖mathematicalBddAbove
Preorder.toLE
Set.FiniteBddBelow.finite
dual

BddBelow

Theorems

NameKindAssumesProvesValidatesDepends On
finite 📖mathematicalBddBelow
Preorder.toLE
Set.FiniteSet.Finite.subset
Finset.finite_toSet
Finset.mem_Ici

Equiv

Definitions

NameCategoryTheorems
IicFinsetSet 📖CompOp
2 mathmath: Preorder.piCongrLeft_comp_restrictLe, Preorder.piCongrLeft_comp_frestrictLe

Finset

Definitions

NameCategoryTheorems
instUniqueSubtypeMemIicBot 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
Icc_bot 📖mathematicalIcc
Bot.bot
OrderBot.toBot
Preorder.toLE
Iic
LocallyFiniteOrder.toLocallyFiniteOrderBot
Icc_bot_top 📖mathematicalIcc
Bot.bot
OrderBot.toBot
Preorder.toLE
BoundedOrder.toOrderBot
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
univ
Icc_bot
Iic_top
Icc_diff_Ico_self 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Finset
instSDiff
Icc
Ico
instSingleton
coe_sdiff
coe_Icc
coe_Ico
Set.Icc_diff_Ico_same
coe_singleton
Icc_diff_Ioc_self 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Finset
instSDiff
Icc
Ioc
instSingleton
coe_sdiff
coe_Icc
coe_Ioc
Set.Icc_diff_Ioc_same
coe_singleton
Icc_diff_Ioo_self 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Finset
instSDiff
Icc
Ioo
instInsert
instSingleton
coe_sdiff
coe_Icc
coe_Ioo
Set.Icc_diff_Ioo_same
coe_insert
coe_singleton
Icc_diff_both 📖mathematicalFinset
instSDiff
Icc
PartialOrder.toPreorder
instInsert
instSingleton
Ioo
coe_sdiff
coe_Icc
coe_insert
coe_singleton
Set.Icc_diff_both
coe_Ioo
Icc_eq_cons_Ico 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Icc
cons
Ico
right_notMem_Ico
right_notMem_Ico
cons_eq_insert
Ico_insert_right
Icc_eq_cons_Ioc 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Icc
cons
Ioc
left_notMem_Ioc
left_notMem_Ioc
cons_eq_insert
Ioc_insert_left
Icc_eq_empty 📖mathematicalPreorder.toLEIcc
Finset
instEmptyCollection
Icc_eq_empty_iff
Icc_eq_empty_iff 📖mathematicalIcc
Finset
instEmptyCollection
Preorder.toLE
coe_eq_empty
coe_Icc
Set.Icc_eq_empty_iff
Icc_eq_empty_of_lt 📖mathematicalPreorder.toLTIcc
Finset
instEmptyCollection
Icc_eq_empty
LT.lt.not_ge
Icc_eq_singleton_iff 📖mathematicalIcc
PartialOrder.toPreorder
Finset
instSingleton
coe_eq_singleton
coe_Icc
Set.Icc_eq_singleton_iff
Icc_erase_left 📖mathematicalerase
Icc
PartialOrder.toPreorder
Ioc
coe_erase
coe_Icc
Set.Icc_diff_left
coe_Ioc
Icc_erase_right 📖mathematicalerase
Icc
PartialOrder.toPreorder
Ico
coe_erase
coe_Icc
Set.Icc_diff_right
coe_Ico
Icc_filter_lt_of_lt_right 📖mathematicalPreorder.toLTfilter
Icc
filter_true_of_mem
lt_of_le_of_lt
mem_Icc
Icc_map_sectL 📖mathematicalmap
Function.Embedding.sectL
Icc
Prod.instPreorder
PartialOrder.toPreorder
Prod.instLocallyFiniteOrder
ext
le_antisymm
Icc_map_sectR 📖mathematicalmap
Function.Embedding.sectR
Icc
Prod.instPreorder
PartialOrder.toPreorder
Prod.instLocallyFiniteOrder
ext
le_antisymm
Icc_min_max 📖mathematicalIcc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
uIcc
Icc_self 📖mathematicalIcc
PartialOrder.toPreorder
Finset
instSingleton
coe_eq_singleton
coe_Icc
Set.Icc_self
Icc_ssubset_Icc_left 📖mathematicalPreorder.toLE
Preorder.toLT
Finset
instHasSSubset
Icc
coe_ssubset
coe_Icc
Set.Icc_ssubset_Icc_left
Icc_ssubset_Icc_right 📖mathematicalPreorder.toLE
Preorder.toLT
Finset
instHasSSubset
Icc
coe_ssubset
coe_Icc
Set.Icc_ssubset_Icc_right
Icc_subset_Icc 📖mathematicalPreorder.toLEFinset
instHasSubset
Icc
coe_Icc
Set.Icc_subset_Icc
Icc_subset_Icc_iff 📖mathematicalPreorder.toLEFinset
instHasSubset
Icc
coe_subset
coe_Icc
Set.Icc_subset_Icc_iff
Icc_subset_Icc_left 📖mathematicalPreorder.toLEFinset
instHasSubset
Icc
Icc_subset_Icc
le_rfl
Icc_subset_Icc_right 📖mathematicalPreorder.toLEFinset
instHasSubset
Icc
Icc_subset_Icc
le_rfl
Icc_subset_Ici_self 📖mathematicalFinset
instHasSubset
Icc
Ici
coe_Icc
coe_Ici
Set.Icc_subset_Ici_self
Icc_subset_Ico_iff 📖mathematicalPreorder.toLEFinset
instHasSubset
Icc
Ico
Preorder.toLT
coe_subset
coe_Icc
coe_Ico
Set.Icc_subset_Ico_iff
Icc_subset_Ico_right 📖mathematicalPreorder.toLTFinset
instHasSubset
Icc
Ico
coe_subset
coe_Icc
coe_Ico
Set.Icc_subset_Ico_right
Icc_subset_Iic_self 📖mathematicalFinset
instHasSubset
Icc
Iic
coe_Icc
coe_Iic
Set.Icc_subset_Iic_self
Icc_subset_Ioc_iff 📖mathematicalPreorder.toLEFinset
instHasSubset
Icc
Ioc
Preorder.toLT
Icc_subset_Ico_iff
LE.le.dual
Icc_subset_Ioo_iff 📖mathematicalPreorder.toLEFinset
instHasSubset
Icc
Ioo
Preorder.toLT
coe_subset
coe_Icc
coe_Ioo
Set.Icc_subset_Ioo_iff
Icc_subset_uIcc 📖mathematicalFinset
instHasSubset
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
Icc_subset_Icc
inf_le_left
le_sup_right
Icc_subset_uIcc' 📖mathematicalFinset
instHasSubset
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
Icc_subset_Icc
inf_le_right
le_sup_left
Icc_top 📖mathematicalIcc
Top.top
OrderTop.toTop
Preorder.toLE
Ici
LocallyFiniteOrder.toLocallyFiniteOrderTop
Ici_bot 📖mathematicalIci
Bot.bot
OrderBot.toBot
Preorder.toLE
univ
ext
Ici_eq_cons_Ioi 📖mathematicalIci
PartialOrder.toPreorder
cons
Ioi
notMem_Ioi_self
notMem_Ioi_self
cons_eq_insert
Ioi_insert
Ici_erase 📖mathematicalerase
Ici
PartialOrder.toPreorder
Ioi
ext
Ici_ssubset_Ici 📖mathematicalFinset
instHasSSubset
Ici
Preorder.toLT
coe_Ici
Ici_subset_Ici 📖mathematicalFinset
instHasSubset
Ici
Preorder.toLE
coe_Ici
Ici_top 📖mathematicalIci
PartialOrder.toPreorder
LocallyFiniteOrder.toLocallyFiniteOrderTop
Top.top
OrderTop.toTop
Preorder.toLE
Finset
instSingleton
Icc_eq_singleton_iff
Ico_bot 📖mathematicalIco
Bot.bot
OrderBot.toBot
Preorder.toLE
Iio
LocallyFiniteOrder.toLocallyFiniteOrderBot
Ico_diff_Ico_left 📖mathematicalFinset
instSDiff
LinearOrder.toDecidableEq
Ico
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Ico_diff_Ico_right 📖mathematicalFinset
instSDiff
LinearOrder.toDecidableEq
Ico
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
Ico_diff_Ioo_self 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
Finset
instSDiff
Ico
Ioo
instSingleton
coe_sdiff
coe_Ico
coe_Ioo
Set.Ico_diff_Ioo_same
coe_singleton
Ico_disjoint_Ico_consecutive 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
Ico
PartialOrder.toPreorder
disjoint_left
LT.lt.not_ge
mem_Ico
Ico_eq_cons_Ioo 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
Ico
cons
Ioo
left_notMem_Ioo
left_notMem_Ioo
cons_eq_insert
Ioo_insert_left
Ico_eq_empty 📖mathematicalPreorder.toLTIco
Finset
instEmptyCollection
Ico_eq_empty_iff
Ico_eq_empty_iff 📖mathematicalIco
Finset
instEmptyCollection
Preorder.toLT
coe_eq_empty
coe_Ico
Set.Ico_eq_empty_iff
Ico_eq_empty_of_le 📖mathematicalPreorder.toLEIco
Finset
instEmptyCollection
Ico_eq_empty
LE.le.not_gt
Ico_erase_left 📖mathematicalerase
Ico
PartialOrder.toPreorder
Ioo
coe_erase
coe_Ico
Set.Ico_diff_left
coe_Ioo
Ico_filter_le 📖mathematicalfilter
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrder.toDecidableLE
Ico
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Ico_filter_le_left 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
filter
Preorder.toLE
Ico
Finset
instSingleton
Ico_filter_le_of_le_left 📖mathematicalPreorder.toLEfilter
Ico
filter_true_of_mem
LE.le.trans
mem_Ico
Ico_filter_le_of_left_le 📖mathematicalPreorder.toLEfilter
Ico
Ico_filter_le_of_right_le 📖mathematicalfilter
Preorder.toLE
Ico
Finset
instEmptyCollection
filter_false_of_mem
LT.lt.not_ge
mem_Ico
Ico_filter_lt 📖mathematicalfilter
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrder.toDecidableLT
Ico
SemilatticeInf.toMin
Ico_filter_lt_of_le_left 📖mathematicalPreorder.toLEfilter
Preorder.toLT
Ico
Finset
instEmptyCollection
filter_false_of_mem
LE.le.not_gt
LE.le.trans
mem_Ico
Ico_filter_lt_of_le_right 📖mathematicalPreorder.toLEfilter
Preorder.toLT
Ico
Ico_filter_lt_of_right_le 📖mathematicalPreorder.toLEfilter
Preorder.toLT
Ico
filter_true_of_mem
LT.lt.trans_le
mem_Ico
Ico_insert_right 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Finset
instInsert
Ico
Icc
coe_insert
coe_Icc
coe_Ico
Set.insert_eq
Set.union_comm
Set.Ico_union_right
Ico_inter_Ico 📖mathematicalFinset
instInter
LinearOrder.toDecidableEq
Ico
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
coe_inter
coe_Ico
Set.Ico_inter_Ico
Ico_inter_Ico_consecutive 📖mathematicalFinset
instInter
Ico
PartialOrder.toPreorder
instEmptyCollection
Disjoint.eq_bot
Ico_disjoint_Ico_consecutive
Ico_map_sectL 📖mathematicalmap
Function.Embedding.sectL
Ico
Prod.instPreorder
PartialOrder.toPreorder
Prod.instLocallyFiniteOrder
ext
le_antisymm
le_of_lt
Ico_map_sectR 📖mathematicalmap
Function.Embedding.sectR
Ico
Prod.instPreorder
PartialOrder.toPreorder
Prod.instLocallyFiniteOrder
ext
le_antisymm
le_of_lt
Ico_self 📖mathematicalIco
Finset
instEmptyCollection
Ico_eq_empty
lt_irrefl
Ico_subset_Icc_self 📖mathematicalFinset
instHasSubset
Ico
Icc
coe_subset
coe_Ico
coe_Icc
Set.Ico_subset_Icc_self
Ico_subset_Ici_self 📖mathematicalFinset
instHasSubset
Ico
Ici
coe_Ico
coe_Ici
Set.Ico_subset_Ici_self
Ico_subset_Ico 📖mathematicalPreorder.toLEFinset
instHasSubset
Ico
coe_Ico
Set.Ico_subset_Ico
Ico_subset_Ico_iff 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instHasSubset
Ico
Preorder.toLE
coe_subset
coe_Ico
Set.Ico_subset_Ico_iff
Ico_subset_Ico_left 📖mathematicalPreorder.toLEFinset
instHasSubset
Ico
Ico_subset_Ico
le_rfl
Ico_subset_Ico_right 📖mathematicalPreorder.toLEFinset
instHasSubset
Ico
Ico_subset_Ico
le_rfl
Ico_subset_Ico_union_Ico 📖mathematicalFinset
instHasSubset
Ico
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instUnion
LinearOrder.toDecidableEq
coe_subset
coe_union
coe_Ico
Set.Ico_subset_Ico_union_Ico
Ico_subset_Iic_self 📖mathematicalFinset
instHasSubset
Ico
Iic
HasSubset.Subset.trans
instIsTransSubset
Ico_subset_Icc_self
Icc_subset_Iic_self
Ico_subset_Iio_self 📖mathematicalFinset
instHasSubset
Ico
Iio
coe_Ico
coe_Iio
Set.Ico_subset_Iio_self
Ico_subset_Ioo_left 📖mathematicalPreorder.toLTFinset
instHasSubset
Ico
Ioo
coe_subset
coe_Ico
coe_Ioo
Set.Ico_subset_Ioo_left
Ico_union_Ico 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Finset
instUnion
LinearOrder.toDecidableEq
Ico
coe_union
coe_Ico
Set.Ico_union_Ico
Ico_union_Ico' 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instUnion
LinearOrder.toDecidableEq
Ico
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
coe_union
coe_Ico
Set.Ico_union_Ico'
Ico_union_Ico_eq_Ico 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instUnion
LinearOrder.toDecidableEq
Ico
coe_union
coe_Ico
Set.Ico_union_Ico_eq_Ico
Iic_bot 📖mathematicalIic
PartialOrder.toPreorder
LocallyFiniteOrder.toLocallyFiniteOrderBot
Bot.bot
OrderBot.toBot
Preorder.toLE
Finset
instSingleton
Icc_eq_singleton_iff
Iic_diff_Ioc 📖mathematicalFinset
instSDiff
LinearOrder.toDecidableEq
Iic
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Ioc
SemilatticeInf.toMin
Iic_diff_Ioc_self_of_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instSDiff
LinearOrder.toDecidableEq
Iic
Ioc
Iic_diff_Ioc
min_eq_left
Iic_disjoint_Ioc 📖mathematicalPreorder.toLEDisjoint
Finset
partialOrder
instOrderBot
Iic
Ioc
disjoint_left
LE.le.not_gt
mem_Iic
lt_of_le_of_lt
mem_Ioc
Iic_eq_cons_Iio 📖mathematicalIic
PartialOrder.toPreorder
cons
Iio
notMem_Iio_self
notMem_Iio_self
cons_eq_insert
Iio_insert
Iic_erase 📖mathematicalerase
Iic
PartialOrder.toPreorder
Iio
ext
Iic_filter_lt_of_lt_right 📖mathematicalPreorder.toLTfilter
Iic
filter_true_of_mem
lt_of_le_of_lt
mem_Iic
Iic_ssubset_Iic 📖mathematicalFinset
instHasSSubset
Iic
Preorder.toLT
coe_Iic
Iic_subset_Iic 📖mathematicalFinset
instHasSubset
Iic
Preorder.toLE
coe_Iic
Iic_top 📖mathematicalIic
Top.top
OrderTop.toTop
Preorder.toLE
univ
ext
Iic_union_Ioc_eq_Iic 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instUnion
LinearOrder.toDecidableEq
Iic
Ioc
Iio_bot 📖mathematicalIio
Bot.bot
OrderBot.toBot
Preorder.toLE
Finset
instEmptyCollection
Iio_eq_empty
isMin_bot
Iio_eq_empty 📖mathematicalIio
Finset
instEmptyCollection
IsMin
Preorder.toLE
Ioi_eq_empty
Iio_filter_lt 📖mathematicalfilter
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrder.toDecidableLT
Iio
SemilatticeInf.toMin
Iio_insert 📖mathematicalFinset
instInsert
Iio
PartialOrder.toPreorder
Iic
ext
Iio_nonempty 📖mathematicalNonempty
Iio
IsMin
Preorder.toLE
Mathlib.Tactic.Contrapose.contrapose_iff₃
Iio_eq_empty
Iio_ssubset_Iio 📖mathematicalPreorder.toLTFinset
instHasSSubset
Iio
coe_Iio
Set.Iio_ssubset_Iio
Iio_subset_Iic_self 📖mathematicalFinset
instHasSubset
Iio
Iic
coe_Iio
coe_Iic
Set.Iio_subset_Iic_self
Iio_subset_Iio 📖mathematicalPreorder.toLEFinset
instHasSubset
Iio
coe_Iio
Set.Iio_subset_Iio
Ioc_diff_Ioo_self 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
Finset
instSDiff
Ioc
Ioo
instSingleton
coe_sdiff
coe_Ioc
coe_Ioo
Set.Ioc_diff_Ioo_same
coe_singleton
Ioc_disjoint_Ioc 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
Ioc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Ioc_inter_Ioc
Ioc_disjoint_Ioc_of_le 📖mathematicalPreorder.toLEDisjoint
Finset
partialOrder
instOrderBot
Ioc
disjoint_left
LE.le.not_gt
LE.le.trans
mem_Ioc
Ioc_eq_cons_Ioo 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
Ioc
cons
Ioo
right_notMem_Ioo
right_notMem_Ioo
cons_eq_insert
Ioo_insert_right
Ioc_eq_empty 📖mathematicalPreorder.toLTIoc
Finset
instEmptyCollection
Ioc_eq_empty_iff
Ioc_eq_empty_iff 📖mathematicalIoc
Finset
instEmptyCollection
Preorder.toLT
coe_eq_empty
coe_Ioc
Set.Ioc_eq_empty_iff
Ioc_eq_empty_of_le 📖mathematicalPreorder.toLEIoc
Finset
instEmptyCollection
Ioc_eq_empty
LE.le.not_gt
Ioc_erase_right 📖mathematicalerase
Ioc
PartialOrder.toPreorder
Ioo
coe_erase
coe_Ioc
Set.Ioc_diff_right
coe_Ioo
Ioc_filter_lt_of_lt_right 📖mathematicalPreorder.toLTfilter
Ioc
filter_true_of_mem
lt_of_le_of_lt
mem_Ioc
Ioc_insert_left 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Finset
instInsert
Ioc
Icc
coe_insert
coe_Ioc
coe_Icc
Set.insert_eq
Set.union_comm
Set.Ioc_union_left
Ioc_inter_Ioc 📖mathematicalFinset
instInter
LinearOrder.toDecidableEq
Ioc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
Ioc_map_sectL 📖mathematicalmap
Function.Embedding.sectL
Ioc
Prod.instPreorder
PartialOrder.toPreorder
Prod.instLocallyFiniteOrder
ext
le_antisymm
le_of_lt
Ioc_map_sectR 📖mathematicalmap
Function.Embedding.sectR
Ioc
Prod.instPreorder
PartialOrder.toPreorder
Prod.instLocallyFiniteOrder
ext
le_antisymm
le_of_lt
Ioc_self 📖mathematicalIoc
Finset
instEmptyCollection
Ioc_eq_empty
lt_irrefl
Ioc_subset_Icc_self 📖mathematicalFinset
instHasSubset
Ioc
Icc
coe_subset
coe_Ioc
coe_Icc
Set.Ioc_subset_Icc_self
Ioc_subset_Ici_self 📖mathematicalFinset
instHasSubset
Ioc
Ici
HasSubset.Subset.trans
instIsTransSubset
Ioc_subset_Icc_self
Icc_subset_Ici_self
Ioc_subset_Iic_self 📖mathematicalFinset
instHasSubset
Ioc
Iic
coe_Ioc
coe_Iic
Set.Ioc_subset_Iic_self
Ioc_subset_Ioc 📖mathematicalPreorder.toLEFinset
instHasSubset
Ioc
coe_Ioc
Set.Ioc_subset_Ioc
Ioc_subset_Ioc_left 📖mathematicalPreorder.toLEFinset
instHasSubset
Ioc
Ioc_subset_Ioc
le_rfl
Ioc_subset_Ioc_right 📖mathematicalPreorder.toLEFinset
instHasSubset
Ioc
Ioc_subset_Ioc
le_rfl
Ioc_subset_Ioi_self 📖mathematicalFinset
instHasSubset
Ioc
Ioi
coe_Ioc
coe_Ioi
Set.Ioc_subset_Ioi_self
Ioc_subset_Ioo_right 📖mathematicalPreorder.toLTFinset
instHasSubset
Ioc
Ioo
coe_subset
coe_Ioc
coe_Ioo
Set.Ioc_subset_Ioo_right
Ioc_top 📖mathematicalIoc
Top.top
OrderTop.toTop
Preorder.toLE
Ioi
LocallyFiniteOrder.toLocallyFiniteOrderTop
Ioc_union_Ioc_eq_Ioc 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instUnion
LinearOrder.toDecidableEq
Ioc
coe_union
coe_Ioc
Set.Ioc_union_Ioc_eq_Ioc
Ioi_disjUnion_Iio 📖mathematicaldisjUnion
Ioi
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Iio
disjoint_Ioi_Iio
Compl.compl
Finset
BooleanAlgebra.toCompl
booleanAlgebra
LinearOrder.toDecidableEq
instSingleton
ext
disjoint_Ioi_Iio
disjUnion_eq_union
Ioi_eq_empty 📖mathematicalIoi
Finset
instEmptyCollection
IsMax
Preorder.toLE
coe_eq_empty
coe_Ioi
Set.Ioi_eq_empty_iff
Ioi_insert 📖mathematicalFinset
instInsert
Ioi
PartialOrder.toPreorder
Ici
ext
Ioi_nonempty 📖mathematicalNonempty
Ioi
IsMax
Preorder.toLE
Mathlib.Tactic.Contrapose.contrapose_iff₃
Ioi_eq_empty
Ioi_ssubset_Ioi 📖mathematicalPreorder.toLTFinset
instHasSSubset
Ioi
coe_Ioi
Set.Ioi_ssubset_Ioi
Ioi_subset_Ici_self 📖mathematicalFinset
instHasSubset
Ioi
Ici
coe_Ioi
coe_Ici
Set.Ioi_subset_Ici_self
Ioi_subset_Ioi 📖mathematicalPreorder.toLEFinset
instHasSubset
Ioi
coe_Ioi
Set.Ioi_subset_Ioi
Ioi_top 📖mathematicalIoi
Top.top
OrderTop.toTop
Preorder.toLE
Finset
instEmptyCollection
Ioi_eq_empty
isMax_top
Ioo_eq_empty 📖mathematicalPreorder.toLTIoo
Finset
instEmptyCollection
eq_empty_iff_forall_notMem
LT.lt.trans
mem_Ioo
Ioo_eq_empty_iff 📖mathematicalIoo
Finset
instEmptyCollection
Preorder.toLT
coe_eq_empty
coe_Ioo
Set.Ioo_eq_empty_iff
Ioo_eq_empty_of_le 📖mathematicalPreorder.toLEIoo
Finset
instEmptyCollection
Ioo_eq_empty
LE.le.not_gt
Ioo_filter_lt 📖mathematicalfilter
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LinearOrder.toDecidableLT
Ioo
SemilatticeInf.toMin
Ioo_insert_left 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
Finset
instInsert
Ioo
Ico
coe_insert
coe_Ioo
coe_Ico
Set.insert_eq
Set.union_comm
Set.Ioo_union_left
Ioo_insert_right 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
Finset
instInsert
Ioo
Ioc
coe_insert
coe_Ioo
coe_Ioc
Set.insert_eq
Set.union_comm
Set.Ioo_union_right
Ioo_map_sectL 📖mathematicalmap
Function.Embedding.sectL
Ioo
Prod.instPreorder
PartialOrder.toPreorder
Prod.instLocallyFiniteOrder
ext
le_antisymm
le_of_lt
Ioo_map_sectR 📖mathematicalmap
Function.Embedding.sectR
Ioo
Prod.instPreorder
PartialOrder.toPreorder
Prod.instLocallyFiniteOrder
ext
le_antisymm
le_of_lt
Ioo_self 📖mathematicalIoo
Finset
instEmptyCollection
Ioo_eq_empty
lt_irrefl
Ioo_subset_Icc_self 📖mathematicalFinset
instHasSubset
Ioo
Icc
HasSubset.Subset.trans
instIsTransSubset
Ioo_subset_Ico_self
Ico_subset_Icc_self
Ioo_subset_Ici_self 📖mathematicalFinset
instHasSubset
Ioo
Ici
HasSubset.Subset.trans
instIsTransSubset
Ioo_subset_Ico_self
Ico_subset_Ici_self
Ioo_subset_Ico_self 📖mathematicalFinset
instHasSubset
Ioo
Ico
coe_subset
coe_Ioo
coe_Ico
Set.Ioo_subset_Ico_self
Ioo_subset_Iic_self 📖mathematicalFinset
instHasSubset
Ioo
Iic
HasSubset.Subset.trans
instIsTransSubset
Ioo_subset_Ioc_self
Ioc_subset_Iic_self
Ioo_subset_Iio_self 📖mathematicalFinset
instHasSubset
Ioo
Iio
coe_Ioo
coe_Iio
Set.Ioo_subset_Iio_self
Ioo_subset_Ioc_self 📖mathematicalFinset
instHasSubset
Ioo
Ioc
coe_subset
coe_Ioo
coe_Ioc
Set.Ioo_subset_Ioc_self
Ioo_subset_Ioi_self 📖mathematicalFinset
instHasSubset
Ioo
Ioi
coe_Ioo
coe_Ioi
Set.Ioo_subset_Ioi_self
Ioo_subset_Ioo 📖mathematicalPreorder.toLEFinset
instHasSubset
Ioo
coe_Ioo
Set.Ioo_subset_Ioo
Ioo_subset_Ioo_left 📖mathematicalPreorder.toLEFinset
instHasSubset
Ioo
Ioo_subset_Ioo
le_rfl
Ioo_subset_Ioo_right 📖mathematicalPreorder.toLEFinset
instHasSubset
Ioo
Ioo_subset_Ioo
le_rfl
card_Ico_eq_card_Icc_sub_one 📖mathematicalcard
Ico
PartialOrder.toPreorder
Icc
right_notMem_Ico
Icc_eq_cons_Ico
card_cons
Ico_eq_empty
LT.lt.le
Icc_eq_empty
card_empty
card_Iio_eq_card_Iic_sub_one 📖mathematicalcard
Iio
PartialOrder.toPreorder
Iic
notMem_Iio_self
Iic_eq_cons_Iio
card_cons
card_Ioc_eq_card_Icc_sub_one 📖mathematicalcard
Ioc
PartialOrder.toPreorder
Icc
card_Ico_eq_card_Icc_sub_one
card_Ioi_eq_card_Ici_sub_one 📖mathematicalcard
Ioi
PartialOrder.toPreorder
Ici
notMem_Ioi_self
Ici_eq_cons_Ioi
card_cons
card_Ioo_eq_card_Icc_sub_two 📖mathematicalcard
Ioo
PartialOrder.toPreorder
Icc
card_Ioo_eq_card_Ico_sub_one
card_Ico_eq_card_Icc_sub_one
card_Ioo_eq_card_Ico_sub_one 📖mathematicalcard
Ioo
PartialOrder.toPreorder
Ico
left_notMem_Ioo
Ico_eq_cons_Ioo
card_cons
Ioo_eq_empty
Ico_eq_empty
card_empty
card_Ioo_eq_card_Ioc_sub_one 📖mathematicalcard
Ioo
PartialOrder.toPreorder
Ioc
card_Ioo_eq_card_Ico_sub_one
disjoint_Ioi_Iio 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
Ioi
Iio
disjoint_left
LT.lt.not_gt
mem_Ioi
mem_Iio
eq_of_mem_uIcc_of_mem_uIcc 📖Finset
instMembership
uIcc
DistribLattice.toLattice
Set.eq_of_mem_uIcc_of_mem_uIcc
eq_of_mem_uIcc_of_mem_uIcc' 📖Finset
instMembership
uIcc
DistribLattice.toLattice
Set.eq_of_mem_uIcc_of_mem_uIcc'
filter_ge_eq_Iic 📖mathematicalfilter
Preorder.toLE
univ
Iic
ext
filter_gt_eq_Iio 📖mathematicalfilter
Preorder.toLT
univ
Iio
ext
filter_le_eq_Ici 📖mathematicalfilter
Preorder.toLE
univ
Ici
ext
filter_le_le_eq_Icc 📖mathematicalfilter
Preorder.toLE
univ
Icc
ext
filter_le_lt_eq_Ico 📖mathematicalfilter
Preorder.toLE
Preorder.toLT
univ
Ico
ext
filter_lt_eq_Ioi 📖mathematicalfilter
Preorder.toLT
univ
Ioi
ext
filter_lt_le_eq_Ioc 📖mathematicalfilter
Preorder.toLT
Preorder.toLE
univ
Ioc
ext
filter_lt_lt_eq_Ioo 📖mathematicalfilter
Preorder.toLT
univ
Ioo
ext
image_subset_Iic_sup 📖mathematicalFinset
instHasSubset
image
Iic
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
mem_Iic
mem_image
le_sup
inf'_Ici 📖mathematicalinf'
Ici
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
nonempty_Ici
ge_antisymm
nonempty_Ici
le_inf'
mem_Ici
inf'_le
le_refl
inf_Ici 📖mathematicalinf
Ici
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
le_antisymm
inf_le
mem_Ici
le_refl
le_inf
left_mem_Icc 📖mathematicalFinset
instMembership
Icc
Preorder.toLE
left_mem_Ico 📖mathematicalFinset
instMembership
Ico
Preorder.toLT
left_mem_uIcc 📖mathematicalFinset
instMembership
uIcc
mem_Icc
inf_le_left
le_sup_left
left_notMem_Ioc 📖mathematicalFinset
instMembership
Ioc
lt_irrefl
mem_Ioc
left_notMem_Ioo 📖mathematicalFinset
instMembership
Ioo
lt_irrefl
mem_Ioo
mem_uIcc' 📖mathematicalFinset
instMembership
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc_eq_union
mem_uIcc_of_ge 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Finset
instMembership
uIcc
Icc_subset_uIcc'
mem_Icc
mem_uIcc_of_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Finset
instMembership
uIcc
Icc_subset_uIcc
mem_Icc
nonempty_Icc 📖mathematicalNonempty
Icc
Preorder.toLE
coe_nonempty
coe_Icc
Set.nonempty_Icc
nonempty_Ici 📖mathematicalNonempty
Ici
mem_Ici
le_rfl
nonempty_Ico 📖mathematicalNonempty
Ico
Preorder.toLT
coe_nonempty
coe_Ico
Set.nonempty_Ico
nonempty_Iic 📖mathematicalNonempty
Iic
mem_Iic
le_rfl
nonempty_Iio 📖mathematicalNonempty
Iio
IsMin
Preorder.toLE
nonempty_Ioc 📖mathematicalNonempty
Ioc
Preorder.toLT
coe_nonempty
coe_Ioc
Set.nonempty_Ioc
nonempty_Ioi 📖mathematicalNonempty
Ioi
IsMax
Preorder.toLE
nonempty_Ioo 📖mathematicalNonempty
Ioo
Preorder.toLT
coe_nonempty
coe_Ioo
Set.nonempty_Ioo
nonempty_uIcc 📖mathematicalNonempty
uIcc
nonempty_Icc
inf_le_sup
notMem_Iio_self 📖mathematicalFinset
instMembership
Iio
PartialOrder.toPreorder
lt_irrefl
mem_Iio
notMem_Ioi_self 📖mathematicalFinset
instMembership
Ioi
PartialOrder.toPreorder
lt_irrefl
mem_Ioi
notMem_uIcc_of_gt 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instMembership
uIcc
mem_uIcc
Set.notMem_uIcc_of_gt
notMem_uIcc_of_lt 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instMembership
uIcc
mem_uIcc
Set.notMem_uIcc_of_lt
right_mem_Icc 📖mathematicalFinset
instMembership
Icc
Preorder.toLE
right_mem_Ioc 📖mathematicalFinset
instMembership
Ioc
Preorder.toLT
right_mem_uIcc 📖mathematicalFinset
instMembership
uIcc
mem_Icc
inf_le_right
le_sup_right
right_notMem_Ico 📖mathematicalFinset
instMembership
Ico
lt_irrefl
mem_Ico
right_notMem_Ioo 📖mathematicalFinset
instMembership
Ioo
lt_irrefl
mem_Ioo
subset_Iic_sup_id 📖mathematicalFinset
instHasSubset
Iic
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
mem_Iic
le_sup
sup'_Iic 📖mathematicalsup'
Iic
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
nonempty_Iic
le_antisymm
nonempty_Iic
sup'_le
mem_Iic
le_sup'
le_refl
sup_Iic 📖mathematicalsup
Iic
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
le_antisymm
sup_le
mem_Iic
le_sup
le_refl
uIcc_comm 📖mathematicaluIccuIcc.eq_1
inf_comm
sup_comm
uIcc_eq_union 📖mathematicaluIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Finset
instUnion
LinearOrder.toDecidableEq
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
coe_injective
coe_uIcc
coe_union
coe_Icc
Set.uIcc_eq_union
uIcc_injective_left 📖mathematicalFinset
uIcc
DistribLattice.toLattice
uIcc_comm
uIcc_injective_right
uIcc_injective_right 📖mathematicalFinset
uIcc
DistribLattice.toLattice
eq_of_mem_uIcc_of_mem_uIcc
ext_iff
left_mem_uIcc
uIcc_map_sectL 📖mathematicalmap
Function.Embedding.sectL
uIcc
Prod.instLattice
Prod.instLocallyFiniteOrder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
ext
inf_of_le_left
sup_of_le_left
le_antisymm
uIcc_map_sectR 📖mathematicalmap
Function.Embedding.sectR
uIcc
Prod.instLattice
Prod.instLocallyFiniteOrder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
ext
inf_of_le_left
sup_of_le_left
le_antisymm
uIcc_of_ge 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
Icc
uIcc.eq_1
inf_eq_right
sup_eq_left
uIcc_of_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
Icc
uIcc.eq_1
inf_eq_left
sup_eq_right
uIcc_of_not_ge 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIcc
Icc
uIcc_of_le
le_of_not_ge
uIcc_of_not_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIcc
Icc
uIcc_of_ge
le_of_not_ge
uIcc_self 📖mathematicaluIcc
Finset
instSingleton
inf_of_le_left
sup_of_le_left
Icc_self
uIcc_subset_Icc 📖mathematicalFinset
instMembership
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
instHasSubset
uIcc
Icc_subset_Icc
le_inf
mem_Icc
sup_le
uIcc_subset_uIcc 📖mathematicalFinset
instMembership
uIcc
instHasSubsetIcc_subset_Icc
le_inf
mem_uIcc
sup_le
uIcc_subset_uIcc_iff_le 📖mathematicalFinset
instHasSubset
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
uIcc_subset_uIcc_iff_le'
uIcc_subset_uIcc_iff_le' 📖mathematicalFinset
instHasSubset
uIcc
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Icc_subset_Icc_iff
inf_le_sup
uIcc_subset_uIcc_iff_mem 📖mathematicalFinset
instHasSubset
uIcc
instMembership
left_mem_uIcc
right_mem_uIcc
uIcc_subset_uIcc
uIcc_subset_uIcc_left 📖mathematicalFinset
instMembership
uIcc
instHasSubsetuIcc_subset_uIcc
left_mem_uIcc
uIcc_subset_uIcc_right 📖mathematicalFinset
instMembership
uIcc
instHasSubsetuIcc_subset_uIcc
right_mem_uIcc
uIcc_subset_uIcc_union_uIcc 📖mathematicalFinset
instHasSubset
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instUnion
LinearOrder.toDecidableEq
coe_subset
coe_uIcc
coe_union
Set.uIcc_subset_uIcc_union_uIcc
uIcc_toDual 📖mathematicaluIcc
OrderDual
OrderDual.instLattice
OrderDual.instLocallyFiniteOrder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
map
Equiv.toEmbedding
Icc_toDual

Finset.Aesop

Theorems

NameKindAssumesProvesValidatesDepends On
nonempty_Icc_of_le 📖mathematicalPreorder.toLEFinset.Nonempty
Finset.Icc
Finset.nonempty_Icc
nonempty_Ico_of_lt 📖mathematicalPreorder.toLTFinset.Nonempty
Finset.Ico
Finset.nonempty_Ico
nonempty_Iio_of_not_isMin 📖mathematicalIsMin
Preorder.toLE
Finset.Nonempty
Finset.Iio
Finset.nonempty_Iio
nonempty_Ioc_of_lt 📖mathematicalPreorder.toLTFinset.Nonempty
Finset.Ioc
Finset.nonempty_Ioc
nonempty_Ioi_of_not_isMax 📖mathematicalIsMax
Preorder.toLE
Finset.Nonempty
Finset.Ioi
Finset.nonempty_Ioi

IsMax

Theorems

NameKindAssumesProvesValidatesDepends On
finsetIoi_eq 📖mathematicalIsMax
Preorder.toLE
Finset.Ioi
Finset
Finset.instEmptyCollection
Finset.Ioi_eq_empty

IsMin

Theorems

NameKindAssumesProvesValidatesDepends On
finsetIio_eq 📖mathematicalIsMin
Preorder.toLE
Finset.Iio
Finset
Finset.instEmptyCollection
Finset.Iio_eq_empty

Set

Definitions

NameCategoryTheorems
fintypeOfMemBounds 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
infinite_iff_exists_gt 📖mathematicalInfinite
Set
instMembership
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Infinite.exists_gt
infinite_of_forall_exists_gt
infinite_iff_exists_lt 📖mathematicalInfinite
Set
instMembership
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Infinite.exists_lt
infinite_of_forall_exists_lt

Set.Infinite

Theorems

NameKindAssumesProvesValidatesDepends On
exists_gt 📖mathematicalSet.InfiniteSet
Set.instMembership
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
not_bddAbove_iff
not_bddAbove
exists_lt 📖mathematicalSet.InfiniteSet
Set.instMembership
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
not_bddBelow_iff
not_bddBelow
not_bddAbove 📖mathematicalSet.InfiniteBddAbove
Preorder.toLE
BddAbove.finite
not_bddBelow 📖mathematicalSet.InfiniteBddBelow
Preorder.toLE
BddBelow.finite

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
antitone_iff_forall_covBy 📖mathematicalAntitone
PartialOrder.toPreorder
Preorder.toLE
monotone_iff_forall_covBy
antitone_iff_forall_wcovBy 📖mathematicalAntitone
Preorder.toLE
monotone_iff_forall_wcovBy
le_iff_reflTransGen_covBy 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Relation.ReflTransGen
CovBy
Preorder.toLT
le_iff_transGen_wcovBy
wcovBy_eq_reflGen_covBy
Relation.transGen_reflGen
le_iff_transGen_wcovBy 📖mathematicalPreorder.toLE
WCovBy
transGen_wcovBy_of_le
WCovBy.le
LE.le.trans
lt_iff_transGen_covBy 📖mathematicalPreorder.toLT
CovBy
transGen_covBy_of_lt
LT.lt.trans
monotone_iff_forall_covBy 📖mathematicalMonotone
PartialOrder.toPreorder
Preorder.toLE
CovBy.le
Relation.reflTransGen_eq_self
Std.Refl.reflexive
instReflLe
transitive_le
Relation.ReflTransGen.lift
le_iff_reflTransGen_covBy
monotone_iff_forall_wcovBy 📖mathematicalMonotone
Preorder.toLE
WCovBy.le
Relation.transGen_eq_self
transitive_le
Relation.TransGen.lift
le_iff_transGen_wcovBy
not_lt_of_denselyOrdered_of_locallyFinite 📖mathematicalPreorder.toLTexists_between
Finset.Icc_ssubset_Icc_right
LT.lt.le
LT.lt.trans
le_rfl
strictAnti_iff_forall_covBy 📖mathematicalStrictAnti
Preorder.toLT
strictMono_iff_forall_covBy
strictMono_iff_forall_covBy 📖mathematicalStrictMono
Preorder.toLT
CovBy.lt
Relation.TransGen.lift
Relation.transGen_eq_self
lt_trans
lt_iff_transGen_covBy
transGen_covBy_of_lt 📖mathematicalPreorder.toLTCovBy
transGen_wcovBy_of_le 📖mathematicalPreorder.toLEWCovBy

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