Documentation Verification Report

Basic

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

Statistics

MetricCount
DefinitionsorderTop, orderBot, instDecidableIsLeast, tacticBddDefault
4
Theoremsdual, exists_ge, insert, inter_of_left, inter_of_right, mono, union, dual, exists_le, insert, inter_of_left, inter_of_right, mono, union, isCofinalFor_fst_image_prod_snd_image, le_of_maximal, le_of_minimal, maximal_iff_isGreatest, minimal_iff_isLeast, isCofinalFor, isCoinitialFor, iscofinalfor, iscoinitialfor, mono_left, mono_right, of_subset, rfl, trans, mono_left, mono_right, of_subset, rfl, trans, bddBelow, dual, exists_between, exists_between', insert, inter_Iic_of_mem, lowerBounds_eq, mono, nonempty, of_subset_of_superset, prod, union, unique, bddAbove, dual, insert, isGreatest_iff_eq, isLUB, lt_iff, mono, nonempty, union, unique, upperBounds_eq, bddAbove, dual, exists_between, exists_between', insert, inter_Ici_of_mem, mono, nonempty, of_subset_of_superset, prod, union, unique, upperBounds_eq, bddBelow, dual, insert, isGLB, isLeast_iff_eq, lowerBounds_eq, lt_iff, mono, nonempty, union, unique, lowerBounds_univ, upperBounds_univ, bddBelow, lowerBounds_univ, bddAbove, upperBounds_univ, bddAbove_lowerBounds, bddBelow_upperBounds, subsingleton_of_isLUB_le_isGLB, bddAbove_Icc, bddAbove_Ico, bddAbove_Iic, bddAbove_Iio, bddAbove_Ioc, bddAbove_Ioo, bddAbove_def, bddAbove_empty, bddAbove_iff_exists_ge, bddAbove_iff_subset_Iic, bddAbove_insert, bddAbove_preimage_ofDual, bddAbove_preimage_toDual, bddAbove_singleton, bddAbove_union, bddBelow_Icc, bddBelow_Ici, bddBelow_Ico, bddBelow_Ioc, bddBelow_Ioi, bddBelow_Ioo, bddBelow_bddAbove_iff_subset_Icc, bddBelow_def, bddBelow_empty, bddBelow_iff_exists_le, bddBelow_iff_subset_Ici, bddBelow_insert, bddBelow_preimage_ofDual, bddBelow_preimage_toDual, bddBelow_singleton, bddBelow_union, bot_mem_lowerBounds, exists_glb_Ioi, exists_lub_Iio, glb_Ioi_eq_self_or_Ioi_eq_Ici, isGLB_Icc, isGLB_Ici, isGLB_Ico, isGLB_Ioc, isGLB_Ioi, isGLB_Ioo, isGLB_congr, isGLB_empty, isGLB_empty_iff, isGLB_iff_le_iff, isGLB_le_isLUB, isGLB_lt_iff, isGLB_lt_isLUB_of_ne, isGLB_pair, isGLB_singleton, isGLB_univ, isGLB_upperBounds, isGreatest_Icc, isGreatest_Iic, isGreatest_Ioc, isGreatest_compl, isGreatest_himp, isGreatest_pair, isGreatest_singleton, isGreatest_top_iff, isGreatest_union_iff, isGreatest_univ, isGreatest_univ_iff, isLUB_Icc, isLUB_Ico, isLUB_Iic, isLUB_Iio, isLUB_Ioc, isLUB_Ioo, isLUB_congr, isLUB_empty, isLUB_empty_iff, isLUB_iff_le_iff, isLUB_le_iff, isLUB_lowerBounds, isLUB_lt_iff, isLUB_pair, isLUB_singleton, isLUB_univ, isLeast_Icc, isLeast_Ici, isLeast_Ico, isLeast_bot_iff, isLeast_hnot, isLeast_pair, isLeast_sdiff, isLeast_singleton, isLeast_union_iff, isLeast_univ, isLeast_univ_iff, le_glb_Ioi, le_isGLB_iff, le_of_isGLB_Ioi, le_of_isLUB_Iio, le_of_isLUB_le_isGLB, lowerBounds_Icc, lowerBounds_Ici, lowerBounds_Ico, lowerBounds_Ioc, lowerBounds_Ioi, lowerBounds_Ioo, lowerBounds_empty, lowerBounds_insert, lowerBounds_le_upperBounds, lowerBounds_mono, lowerBounds_mono_mem, lowerBounds_mono_of_isCoinitialFor, lowerBounds_mono_set, lowerBounds_prod, lowerBounds_singleton, lowerBounds_union, lt_isGLB_iff, lt_isLUB_iff, lub_Iio_eq_self_or_Iio_eq_Iic, lub_Iio_le, maximal_iff_isGreatest, mem_lowerBounds, mem_lowerBounds_iff_subset_Ici, mem_upperBounds, mem_upperBounds_iff_subset_Iic, minimal_iff_isLeast, nonempty_of_not_bddAbove, nonempty_of_not_bddBelow, not_bddAbove_iff, not_bddAbove_iff', not_bddAbove_univ, not_bddBelow_iff, not_bddBelow_iff', not_bddBelow_univ, subset_lowerBounds_upperBounds, subset_upperBounds_lowerBounds, top_mem_upperBounds, union_lowerBounds_subset_lowerBounds_inter, union_upperBounds_subset_upperBounds_inter, upperBounds_Icc, upperBounds_Ico, upperBounds_Iic, upperBounds_Iio, upperBounds_Ioc, upperBounds_Ioo, upperBounds_empty, upperBounds_insert, upperBounds_mono, upperBounds_mono_mem, upperBounds_mono_of_isCofinalFor, upperBounds_mono_set, upperBounds_prod, upperBounds_singleton, upperBounds_union
239
Total243

BddAbove

Theorems

NameKindAssumesProvesValidatesDepends On
dual 📖mathematicalBddAbove
Preorder.toLE
BddBelow
OrderDual
OrderDual.instLE
Set.preimage
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
exists_ge 📖BddAbove
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
bddAbove_iff_exists_ge
insert 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instInsert
bddAbove_insert
inter_of_left 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instInter
mono
Set.inter_subset_left
inter_of_right 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instInter
mono
Set.inter_subset_right
mono 📖Set
Set.instHasSubset
BddAbove
Preorder.toLE
Set.Nonempty.mono
upperBounds_mono_set
union 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instUnion
exists_ge_ge
eq_1
upperBounds_union
upperBounds_mono_mem

BddBelow

Theorems

NameKindAssumesProvesValidatesDepends On
dual 📖mathematicalBddBelow
Preorder.toLE
BddAbove
OrderDual
OrderDual.instLE
Set.preimage
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
exists_le 📖BddBelow
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
bddBelow_iff_exists_le
insert 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instInsert
bddBelow_insert
inter_of_left 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instInter
mono
Set.inter_subset_left
inter_of_right 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instInter
mono
Set.inter_subset_right
mono 📖Set
Set.instHasSubset
BddBelow
Preorder.toLE
Set.Nonempty.mono
lowerBounds_mono_set
union 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instUnion
exists_le_le
eq_1
lowerBounds_union
lowerBounds_mono_mem

DirectedOn

Theorems

NameKindAssumesProvesValidatesDepends On
isCofinalFor_fst_image_prod_snd_image 📖mathematicalDirectedOn
Prod.instLE_mathlib
Preorder.toLE
IsCofinalFor
SProd.sprod
Set
Set.instSProd
Set.image
le_of_maximal 📖DirectedOn
Preorder.toLE
Maximal
Set
Set.instMembership
LE.le.trans
le_of_minimal 📖DirectedOn
Preorder.toLE
Minimal
Set
Set.instMembership
LE.le.trans
maximal_iff_isGreatest 📖mathematicalDirectedOn
Preorder.toLE
Maximal
Set
Set.instMembership
IsGreatest
minimal_iff_isLeast
minimal_iff_isLeast 📖mathematicalDirectedOn
Preorder.toLE
Minimal
Set
Set.instMembership
IsLeast
le_of_minimal

HasSubset.Subset

Theorems

NameKindAssumesProvesValidatesDepends On
isCofinalFor 📖mathematicalSet
Set.instHasSubset
IsCofinalFor
Preorder.toLE
IsCofinalFor.of_subset
isCoinitialFor 📖mathematicalSet
Set.instHasSubset
IsCoinitialFor
Preorder.toLE
IsCoinitialFor.of_subset
iscofinalfor 📖mathematicalSet
Set.instHasSubset
IsCofinalFor
Preorder.toLE
IsCofinalFor.of_subset
iscoinitialfor 📖mathematicalSet
Set.instHasSubset
IsCoinitialFor
Preorder.toLE
IsCoinitialFor.of_subset

IsCofinalFor

Theorems

NameKindAssumesProvesValidatesDepends On
mono_left 📖Set
Set.instHasSubset
IsCofinalFor
Preorder.toLE
trans
HasSubset.Subset.isCofinalFor
mono_right 📖Set
Set.instHasSubset
IsCofinalFor
Preorder.toLE
trans
HasSubset.Subset.isCofinalFor
of_subset 📖mathematicalSet
Set.instHasSubset
IsCofinalFor
Preorder.toLE
le_rfl
rfl 📖mathematicalIsCofinalFor
Preorder.toLE
of_subset
Set.Subset.rfl
trans 📖IsCofinalFor
Preorder.toLE
LE.le.trans

IsCoinitialFor

Theorems

NameKindAssumesProvesValidatesDepends On
mono_left 📖Set
Set.instHasSubset
IsCoinitialFor
Preorder.toLE
trans
HasSubset.Subset.isCoinitialFor
mono_right 📖Set
Set.instHasSubset
IsCoinitialFor
Preorder.toLE
trans
HasSubset.Subset.isCoinitialFor
of_subset 📖mathematicalSet
Set.instHasSubset
IsCoinitialFor
Preorder.toLE
le_rfl
rfl 📖mathematicalIsCoinitialFor
Preorder.toLE
of_subset
Set.Subset.rfl
trans 📖IsCoinitialFor
Preorder.toLE
LE.le.trans'

IsGLB

Theorems

NameKindAssumesProvesValidatesDepends On
bddBelow 📖mathematicalIsGLB
Preorder.toLE
BddBelow
dual 📖mathematicalIsGLB
Preorder.toLE
IsLUB
OrderDual
OrderDual.instLE
Set.preimage
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
OrderDual.toDual
exists_between 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
Set
Set.instMembership
isGLB_lt_iff
exists_between' 📖IsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Preorder.toLT
exists_between
LE.le.lt_of_ne
insert 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Set
Set.instInsert
SemilatticeInf.toMin
Set.insert_eq
union
isGLB_singleton
inter_Iic_of_mem 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.instInter
Set.Iic
le_rfl
le_total
LE.le.trans'
lowerBounds_eq 📖mathematicalIsGLB
Preorder.toLE
lowerBounds
Set.Iic
Set.ext
lowerBounds_mono_mem
mono 📖IsGLB
Preorder.toLE
Set
Set.instHasSubset
IsGreatest.mono
lowerBounds_mono_set
nonempty 📖mathematicalIsGLB
Preorder.toLE
Set.NonemptySet.nonempty_iff_ne_empty
not_isTop
lowerBounds_empty
Set.mem_univ
of_subset_of_superset 📖IsGLB
Preorder.toLE
Set
Set.instHasSubset
lowerBounds_mono_set
upperBounds_mono_set
prod 📖mathematicalSet.Nonempty
IsGLB
Preorder.toLE
Prod.instLE_mathlib
SProd.sprod
Set
Set.instSProd
lowerBounds_prod
Set.mem_prod
union 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Set
Set.instUnion
SemilatticeInf.toMin
inf_le_of_left_le
inf_le_of_right_le
le_inf
unique 📖IsGLB
Preorder.toLE
PartialOrder.toPreorder
IsGreatest.unique

IsGreatest

Definitions

NameCategoryTheorems
orderTop 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
bddAbove 📖mathematicalIsGreatest
Preorder.toLE
BddAbove
dual 📖mathematicalIsGreatest
Preorder.toLE
IsLeast
OrderDual
OrderDual.instLE
Set.preimage
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
OrderDual.toDual
insert 📖mathematicalIsGreatest
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instInsert
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Set.insert_eq
union
isGreatest_singleton
isGreatest_iff_eq 📖IsGreatest
Preorder.toLE
PartialOrder.toPreorder
unique
isLUB 📖mathematicalIsGreatest
Preorder.toLE
IsLUB
lt_iff 📖mathematicalIsGreatest
Preorder.toLE
Preorder.toLTLE.le.trans_lt
mono 📖IsGreatest
Preorder.toLE
Set
Set.instHasSubset
nonempty 📖mathematicalIsGreatest
Preorder.toLE
Set.Nonempty
union 📖mathematicalIsGreatest
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instUnion
SemilatticeSup.toMax
le_total
sup_of_le_left
Set.mem_union
sup_of_le_right
IsLUB.union
isLUB
unique 📖IsGreatest
Preorder.toLE
PartialOrder.toPreorder
ge_antisymm
upperBounds_eq 📖mathematicalIsGreatest
Preorder.toLE
upperBounds
Set.Ici
IsLUB.upperBounds_eq
isLUB

IsLUB

Theorems

NameKindAssumesProvesValidatesDepends On
bddAbove 📖mathematicalIsLUB
Preorder.toLE
BddAbove
dual 📖mathematicalIsLUB
Preorder.toLE
IsGLB
OrderDual
OrderDual.instLE
Set.preimage
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
OrderDual.toDual
exists_between 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
Set
Set.instMembership
lt_isLUB_iff
exists_between' 📖IsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Preorder.toLT
exists_between
LE.le.lt_of_ne
insert 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Set
Set.instInsert
SemilatticeSup.toMax
Set.insert_eq
union
isLUB_singleton
inter_Ici_of_mem 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.instInter
Set.Ici
le_rfl
le_total
LE.le.trans
mono 📖IsLUB
Preorder.toLE
Set
Set.instHasSubset
IsLeast.mono
upperBounds_mono_set
nonempty 📖mathematicalIsLUB
Preorder.toLE
Set.NonemptySet.nonempty_iff_ne_empty
not_isBot
upperBounds_empty
Set.mem_univ
of_subset_of_superset 📖IsLUB
Preorder.toLE
Set
Set.instHasSubset
upperBounds_mono_set
lowerBounds_mono_set
prod 📖mathematicalSet.Nonempty
IsLUB
Preorder.toLE
Prod.instLE_mathlib
SProd.sprod
Set
Set.instSProd
upperBounds_prod
union 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Set
Set.instUnion
SemilatticeSup.toMax
le_sup_of_le_left
le_sup_of_le_right
sup_le
unique 📖IsLUB
Preorder.toLE
PartialOrder.toPreorder
IsLeast.unique
upperBounds_eq 📖mathematicalIsLUB
Preorder.toLE
upperBounds
Set.Ici
Set.ext
upperBounds_mono_mem

IsLeast

Definitions

NameCategoryTheorems
orderBot 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
bddBelow 📖mathematicalIsLeast
Preorder.toLE
BddBelow
dual 📖mathematicalIsLeast
Preorder.toLE
IsGreatest
OrderDual
OrderDual.instLE
Set.preimage
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
OrderDual.toDual
insert 📖mathematicalIsLeast
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instInsert
SemilatticeInf.toMin
Lattice.toSemilatticeInf
Set.insert_eq
union
isLeast_singleton
isGLB 📖mathematicalIsLeast
Preorder.toLE
IsGLB
isLeast_iff_eq 📖IsLeast
Preorder.toLE
PartialOrder.toPreorder
unique
lowerBounds_eq 📖mathematicalIsLeast
Preorder.toLE
lowerBounds
Set.Iic
IsGLB.lowerBounds_eq
isGLB
lt_iff 📖mathematicalIsLeast
Preorder.toLE
Preorder.toLTLE.le.trans_lt'
mono 📖IsLeast
Preorder.toLE
Set
Set.instHasSubset
nonempty 📖mathematicalIsLeast
Preorder.toLE
Set.Nonempty
union 📖mathematicalIsLeast
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instUnion
SemilatticeInf.toMin
le_total
inf_of_le_left
inf_of_le_right
IsGLB.union
isGLB
unique 📖IsLeast
Preorder.toLE
PartialOrder.toPreorder
le_antisymm

Nat

Definitions

NameCategoryTheorems
instDecidableIsLeast 📖CompOp

NoBotOrder

Theorems

NameKindAssumesProvesValidatesDepends On
lowerBounds_univ 📖mathematicallowerBounds
Preorder.toLE
Set.univ
Set
Set.instEmptyCollection
Set.eq_empty_of_subset_empty
not_isBot
Set.mem_univ

NoTopOrder

Theorems

NameKindAssumesProvesValidatesDepends On
upperBounds_univ 📖mathematicalupperBounds
Preorder.toLE
Set.univ
Set
Set.instEmptyCollection
Set.eq_empty_of_subset_empty
not_isTop
Set.mem_univ

OrderBot

Theorems

NameKindAssumesProvesValidatesDepends On
bddBelow 📖mathematicalBddBelow
Preorder.toLE
bot_le
lowerBounds_univ 📖mathematicallowerBounds
Preorder.toLE
PartialOrder.toPreorder
Set.univ
Set
Set.instSingletonSet
Bot.bot
toBot
IsLeast.lowerBounds_eq
isLeast_univ
Set.Iic_bot

OrderTop

Theorems

NameKindAssumesProvesValidatesDepends On
bddAbove 📖mathematicalBddAbove
Preorder.toLE
le_top
upperBounds_univ 📖mathematicalupperBounds
Preorder.toLE
PartialOrder.toPreorder
Set.univ
Set
Set.instSingletonSet
Top.top
toTop
IsGreatest.upperBounds_eq
isGreatest_univ
Set.Ici_top

Set

Theorems

NameKindAssumesProvesValidatesDepends On
subsingleton_of_isLUB_le_isGLB 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
IsLUB
Subsingletonle_antisymm
le_of_isLUB_le_isGLB

Set.Nonempty

Theorems

NameKindAssumesProvesValidatesDepends On
bddAbove_lowerBounds 📖mathematicalSet.NonemptyBddAbove
Preorder.toLE
lowerBounds
mono
subset_upperBounds_lowerBounds
bddBelow_upperBounds 📖mathematicalSet.NonemptyBddBelow
Preorder.toLE
upperBounds
mono
subset_lowerBounds_upperBounds

(root)

Definitions

NameCategoryTheorems
tacticBddDefault 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
bddAbove_Icc 📖mathematicalBddAbove
Preorder.toLE
Set.Icc
bddAbove_Ico 📖mathematicalBddAbove
Preorder.toLE
Set.Ico
BddAbove.mono
Set.Ico_subset_Icc_self
bddAbove_Icc
bddAbove_Iic 📖mathematicalBddAbove
Preorder.toLE
Set.Iic
IsLUB.bddAbove
isLUB_Iic
bddAbove_Iio 📖mathematicalBddAbove
Preorder.toLE
Set.Iio
le_of_lt
bddAbove_Ioc 📖mathematicalBddAbove
Preorder.toLE
Set.Ioc
BddAbove.mono
Set.Ioc_subset_Icc_self
bddAbove_Icc
bddAbove_Ioo 📖mathematicalBddAbove
Preorder.toLE
Set.Ioo
BddAbove.mono
Set.Ioo_subset_Icc_self
bddAbove_Icc
bddAbove_def 📖mathematicalBddAbove
Preorder.toLE
bddAbove_empty 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instEmptyCollection
upperBounds_empty
bddAbove_iff_exists_ge 📖mathematicalBddAbove
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
bddAbove_def
exists_ge_and_iff_exists
Monotone.ball
monotone_le
bddAbove_iff_subset_Iic 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instHasSubset
Set.Iic
bddAbove_insert 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instInsert
bddAbove_preimage_ofDual 📖mathematicalBddAbove
OrderDual
OrderDual.instLE
Preorder.toLE
Set.preimage
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
BddBelow
bddAbove_preimage_toDual 📖mathematicalBddAbove
Preorder.toLE
Set.preimage
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
BddBelow
OrderDual.instLE
bddAbove_singleton 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instSingletonSet
IsLUB.bddAbove
isLUB_singleton
bddAbove_union 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instUnion
BddAbove.mono
Set.subset_union_left
Set.subset_union_right
BddAbove.union
bddBelow_Icc 📖mathematicalBddBelow
Preorder.toLE
Set.Icc
bddBelow_Ici 📖mathematicalBddBelow
Preorder.toLE
Set.Ici
IsGLB.bddBelow
isGLB_Ici
bddBelow_Ico 📖mathematicalBddBelow
Preorder.toLE
Set.Ico
BddBelow.mono
Set.Ico_subset_Icc_self
bddBelow_Icc
bddBelow_Ioc 📖mathematicalBddBelow
Preorder.toLE
Set.Ioc
BddBelow.mono
Set.Ioc_subset_Icc_self
bddBelow_Icc
bddBelow_Ioi 📖mathematicalBddBelow
Preorder.toLE
Set.Ioi
le_of_lt
bddBelow_Ioo 📖mathematicalBddBelow
Preorder.toLE
Set.Ioo
BddBelow.mono
Set.Ioo_subset_Icc_self
bddBelow_Icc
bddBelow_bddAbove_iff_subset_Icc 📖mathematicalBddBelow
Preorder.toLE
BddAbove
Set
Set.instHasSubset
Set.Icc
Set.Ici_inter_Iic
bddBelow_def 📖mathematicalBddBelow
Preorder.toLE
bddBelow_empty 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instEmptyCollection
lowerBounds_empty
Set.univ_nonempty
bddBelow_iff_exists_le 📖mathematicalBddBelow
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
bddAbove_iff_exists_ge
bddBelow_iff_subset_Ici 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instHasSubset
Set.Ici
bddBelow_insert 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instInsert
bddBelow_union
bddBelow_singleton
bddBelow_preimage_ofDual 📖mathematicalBddBelow
OrderDual
OrderDual.instLE
Preorder.toLE
Set.preimage
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
BddAbove
bddBelow_preimage_toDual 📖mathematicalBddBelow
Preorder.toLE
Set.preimage
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
BddAbove
OrderDual.instLE
bddBelow_singleton 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instSingletonSet
IsGLB.bddBelow
isGLB_singleton
bddBelow_union 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instUnion
BddBelow.mono
Set.subset_union_left
Set.subset_union_right
BddBelow.union
bot_mem_lowerBounds 📖mathematicalSet
Set.instMembership
lowerBounds
Preorder.toLE
Bot.bot
OrderBot.toBot
bot_le
exists_glb_Ioi 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ioi
le_of_lt
mem_upperBounds
Mathlib.Tactic.Push.not_exists
Mathlib.Tactic.Push.not_and_eq
not_lt
exists_lub_Iio 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Iio
le_of_lt
mem_lowerBounds
Mathlib.Tactic.Push.not_and_eq
glb_Ioi_eq_self_or_Ioi_eq_Ici 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
Set.Ioi
Set.Icieq_or_lt_of_le'
le_of_isGLB_Ioi
Set.ext
lt_of_le_of_lt'
isGLB_Icc 📖mathematicalPreorder.toLEIsGLB
Set.Icc
IsLeast.isGLB
isLeast_Icc
isGLB_Ici 📖mathematicalIsGLB
Preorder.toLE
Set.Ici
IsLeast.isGLB
isLeast_Ici
isGLB_Ico 📖mathematicalPreorder.toLTIsGLB
Preorder.toLE
Set.Ico
IsLeast.isGLB
isLeast_Ico
isGLB_Ioc 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
IsGLB
Preorder.toLE
Set.Ioc
IsGLB.of_subset_of_superset
isGLB_Ioo
isGLB_Icc
LT.lt.le
Set.Ioo_subset_Ioc_self
Set.Ioc_subset_Icc_self
isGLB_Ioi 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ioi
le_of_lt
le_of_forall_gt_imp_ge_of_dense
isGLB_Ioo 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
IsGLB
Preorder.toLE
Set.Ioo
LT.lt.le
eq_or_lt_of_le
le_sup_right
le_sup_left
exists_between
not_lt_of_ge
sup_le
LT.lt.trans_le
LE.le.trans
isGLB_congr 📖mathematicallowerBounds
Preorder.toLE
IsGLBIsGLB.eq_1
isGLB_empty 📖mathematicalIsGLB
Preorder.toLE
Set
Set.instEmptyCollection
Top.top
OrderTop.toTop
isGLB_empty_iff
isTop_top
isGLB_empty_iff 📖mathematicalIsGLB
Preorder.toLE
Set
Set.instEmptyCollection
IsTop
lowerBounds_empty
isGLB_iff_le_iff 📖mathematicalIsGLB
Preorder.toLE
Set
Set.instMembership
lowerBounds
le_isGLB_iff
le_rfl
isGLB_le_isLUB 📖IsGLB
Preorder.toLE
IsLUB
Set.Nonempty
lowerBounds_le_upperBounds
isGLB_lt_iff 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
Set
Set.instMembership
not_le
le_isGLB_iff
mem_lowerBounds
isGLB_lt_isLUB_of_ne 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
IsLUB
Set
Set.instMembership
Preorder.toLTlt_iff_le_not_ge
lowerBounds_le_upperBounds
Set.subsingleton_of_isLUB_le_isGLB
isGLB_pair 📖mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Set
Set.instInsert
Set.instSingletonSet
SemilatticeInf.toMin
IsGLB.insert
isGLB_singleton
isGLB_singleton 📖mathematicalIsGLB
Preorder.toLE
Set
Set.instSingletonSet
IsLeast.isGLB
isLeast_singleton
isGLB_univ 📖mathematicalIsGLB
Preorder.toLE
Set.univ
Bot.bot
OrderBot.toBot
IsLeast.isGLB
isLeast_univ
isGLB_upperBounds 📖mathematicalIsGLB
Preorder.toLE
upperBounds
IsLUB
subset_lowerBounds_upperBounds
IsLeast.isGLB
isGreatest_Icc 📖mathematicalPreorder.toLEIsGreatest
Set.Icc
Set.right_mem_Icc
isGreatest_Iic 📖mathematicalIsGreatest
Preorder.toLE
Set.Iic
Set.self_mem_Iic
isGreatest_Ioc 📖mathematicalPreorder.toLTIsGreatest
Preorder.toLE
Set.Ioc
Set.right_mem_Ioc
isGreatest_compl 📖mathematicalIsGreatest
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
setOf
Disjoint
HeytingAlgebra.toOrderBot
Compl.compl
HeytingAlgebra.toCompl
himp_bot
isGreatest_himp
isGreatest_himp 📖mathematicalIsGreatest
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedHeytingAlgebra.toLattice
setOf
SemilatticeInf.toMin
HImp.himp
GeneralizedHeytingAlgebra.toHImp
himp_inf_self
isGreatest_pair 📖mathematicalIsGreatest
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instInsert
Set.instSingletonSet
SemilatticeSup.toMax
Lattice.toSemilatticeSup
IsGreatest.insert
isGreatest_singleton
isGreatest_singleton 📖mathematicalIsGreatest
Preorder.toLE
Set
Set.instSingletonSet
Set.mem_singleton
le_of_eq
Set.eq_of_mem_singleton
isGreatest_top_iff 📖mathematicalIsGreatest
Preorder.toLE
Top.top
OrderTop.toTop
Set
Set.instMembership
top_mem_upperBounds
isGreatest_union_iff 📖mathematicalIsGreatest
Preorder.toLE
Set
Set.instUnion
Set.instMembership
upperBounds
Set.mem_union
upperBounds_union
Set.mem_inter_iff
isGreatest_univ 📖mathematicalIsGreatest
Preorder.toLE
Set.univ
Top.top
OrderTop.toTop
isGreatest_univ_iff
isTop_top
isGreatest_univ_iff 📖mathematicalIsGreatest
Preorder.toLE
Set.univ
IsTop
isLUB_Icc 📖mathematicalPreorder.toLEIsLUB
Set.Icc
IsGreatest.isLUB
isGreatest_Icc
isLUB_Ico 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
IsLUB
Preorder.toLE
Set.Ico
Set.Ioc_toDual
isGLB_Ioc
OrderDual.denselyOrdered
LT.lt.dual
isLUB_Iic 📖mathematicalIsLUB
Preorder.toLE
Set.Iic
IsGreatest.isLUB
isGreatest_Iic
isLUB_Iio 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Iio
le_of_lt
le_of_forall_lt_imp_le_of_dense
isLUB_Ioc 📖mathematicalPreorder.toLTIsLUB
Preorder.toLE
Set.Ioc
IsGreatest.isLUB
isGreatest_Ioc
isLUB_Ioo 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
IsLUB
Preorder.toLE
Set.Ioo
Set.Ioo_toDual
isGLB_Ioo
OrderDual.denselyOrdered
LT.lt.dual
isLUB_congr 📖mathematicalupperBounds
Preorder.toLE
IsLUBIsLUB.eq_1
isLUB_empty 📖mathematicalIsLUB
Preorder.toLE
Set
Set.instEmptyCollection
Bot.bot
OrderBot.toBot
isLUB_empty_iff
isBot_bot
isLUB_empty_iff 📖mathematicalIsLUB
Preorder.toLE
Set
Set.instEmptyCollection
IsBot
upperBounds_empty
isLeast_univ_iff
isLUB_iff_le_iff 📖mathematicalIsLUB
Preorder.toLE
Set
Set.instMembership
upperBounds
isLUB_le_iff
le_rfl
isLUB_le_iff 📖mathematicalIsLUB
Preorder.toLE
Set
Set.instMembership
upperBounds
IsLUB.upperBounds_eq
isLUB_lowerBounds 📖mathematicalIsLUB
Preorder.toLE
lowerBounds
IsGLB
subset_upperBounds_lowerBounds
IsGreatest.isLUB
isLUB_lt_iff 📖mathematicalIsLUB
Preorder.toLE
Preorder.toLT
Set
Set.instMembership
upperBounds
lt_of_le_of_lt
isLUB_pair 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Set
Set.instInsert
Set.instSingletonSet
SemilatticeSup.toMax
IsLUB.insert
isLUB_singleton
isLUB_singleton 📖mathematicalIsLUB
Preorder.toLE
Set
Set.instSingletonSet
IsGreatest.isLUB
isGreatest_singleton
isLUB_univ 📖mathematicalIsLUB
Preorder.toLE
Set.univ
Top.top
OrderTop.toTop
IsGreatest.isLUB
isGreatest_univ
isLeast_Icc 📖mathematicalPreorder.toLEIsLeast
Set.Icc
Set.left_mem_Icc
isLeast_Ici 📖mathematicalIsLeast
Preorder.toLE
Set.Ici
Set.self_mem_Ici
isLeast_Ico 📖mathematicalPreorder.toLTIsLeast
Preorder.toLE
Set.Ico
Set.left_mem_Ico
isLeast_bot_iff 📖mathematicalIsLeast
Preorder.toLE
Bot.bot
OrderBot.toBot
Set
Set.instMembership
bot_mem_lowerBounds
isLeast_hnot 📖mathematicalIsLeast
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
setOf
Codisjoint
CoheytingAlgebra.toOrderTop
HNot.hnot
CoheytingAlgebra.toHNot
CoheytingAlgebra.top_sdiff
isLeast_sdiff
isLeast_pair 📖mathematicalIsLeast
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instInsert
Set.instSingletonSet
SemilatticeInf.toMin
Lattice.toSemilatticeInf
IsLeast.insert
isLeast_singleton
isLeast_sdiff 📖mathematicalIsLeast
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
setOf
SemilatticeSup.toMax
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toSDiff
sup_sdiff_self
isLeast_singleton 📖mathematicalIsLeast
Preorder.toLE
Set
Set.instSingletonSet
Set.mem_singleton
ge_of_eq
Set.eq_of_mem_singleton
isLeast_union_iff 📖mathematicalIsLeast
Preorder.toLE
Set
Set.instUnion
Set.instMembership
lowerBounds
lowerBounds_union
isLeast_univ 📖mathematicalIsLeast
Preorder.toLE
Set.univ
Bot.bot
OrderBot.toBot
isLeast_univ_iff
isBot_bot
isLeast_univ_iff 📖mathematicalIsLeast
Preorder.toLE
Set.univ
IsBot
Set.mem_univ
mem_lowerBounds
le_glb_Ioi 📖IsGLB
Preorder.toLE
Set.Ioi
le_of_isGLB_Ioi
le_isGLB_iff 📖mathematicalIsGLB
Preorder.toLE
Set
Set.instMembership
lowerBounds
IsGLB.lowerBounds_eq
le_of_isGLB_Ioi 📖IsGLB
Preorder.toLE
Set.Ioi
le_isGLB_iff
le_of_lt
le_of_isLUB_Iio 📖IsLUB
Preorder.toLE
Set.Iio
isLUB_le_iff
le_of_lt
le_of_isLUB_le_isGLB 📖IsGLB
Preorder.toLE
IsLUB
Set
Set.instMembership
lowerBounds_Icc 📖mathematicalPreorder.toLElowerBounds
Set.Icc
Set.Iic
IsGLB.lowerBounds_eq
isGLB_Icc
lowerBounds_Ici 📖mathematicallowerBounds
Preorder.toLE
Set.Ici
Set.Iic
IsGLB.lowerBounds_eq
isGLB_Ici
lowerBounds_Ico 📖mathematicalPreorder.toLTlowerBounds
Preorder.toLE
Set.Ico
Set.Iic
IsGLB.lowerBounds_eq
isGLB_Ico
lowerBounds_Ioc 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
lowerBounds
Preorder.toLE
Set.Ioc
Set.Iic
IsGLB.lowerBounds_eq
isGLB_Ioc
lowerBounds_Ioi 📖mathematicallowerBounds
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ioi
Set.Iic
IsGLB.lowerBounds_eq
isGLB_Ioi
lowerBounds_Ioo 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
lowerBounds
Preorder.toLE
Set.Ioo
Set.Iic
IsGLB.lowerBounds_eq
isGLB_Ioo
lowerBounds_empty 📖mathematicallowerBounds
Preorder.toLE
Set
Set.instEmptyCollection
Set.univ
Set.forall_mem_empty
Set.eq_univ_iff_forall
forall_true_iff
lowerBounds_insert 📖mathematicallowerBounds
Preorder.toLE
Set
Set.instInsert
Set.instInter
Set.Iic
Set.insert_eq
lowerBounds_union
lowerBounds_singleton
lowerBounds_le_upperBounds 📖Set
Set.instMembership
lowerBounds
Preorder.toLE
upperBounds
Set.Nonempty
le_trans
lowerBounds_mono 📖Set
Set.instHasSubset
Preorder.toLE
Set.instMembership
lowerBounds
lowerBounds_mono_set
lowerBounds_mono_mem
lowerBounds_mono_mem 📖Preorder.toLE
Set
Set.instMembership
lowerBounds
ge_trans
lowerBounds_mono_of_isCoinitialFor 📖mathematicalIsCoinitialFor
Preorder.toLE
Set
Set.instHasSubset
lowerBounds
LE.le.trans'
lowerBounds_mono_set 📖mathematicalSet
Set.instHasSubset
lowerBounds
Preorder.toLE
lowerBounds_prod 📖mathematicalSet.NonemptylowerBounds
Prod.instLE_mathlib
Preorder.toLE
SProd.sprod
Set
Set.instSProd
Set.ext
Set.mem_prod
Prod.le_def
nonempty_subtype
Set.nonempty_coe_sort
lowerBounds_singleton 📖mathematicallowerBounds
Preorder.toLE
Set
Set.instSingletonSet
Set.Iic
IsGLB.lowerBounds_eq
isGLB_singleton
lowerBounds_union 📖mathematicallowerBounds
Preorder.toLE
Set
Set.instUnion
Set.instInter
Set.Subset.antisymm
lt_isGLB_iff 📖mathematicalIsGLB
Preorder.toLE
Preorder.toLT
Set
Set.instMembership
lowerBounds
lt_of_le_of_lt'
lt_isLUB_iff 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
Set
Set.instMembership
isLUB_le_iff
lub_Iio_eq_self_or_Iio_eq_Iic 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
Set.Iio
Set.Iiceq_or_lt_of_le
le_of_isLUB_Iio
Set.ext
lt_of_le_of_lt
lub_Iio_le 📖IsLUB
Preorder.toLE
Set.Iio
le_of_isLUB_Iio
maximal_iff_isGreatest 📖mathematicalMaximal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
IsGreatest
DirectedOn.maximal_iff_isGreatest
Std.Total.directedOn
LE.total
mem_lowerBounds 📖mathematicalSet
Set.instMembership
lowerBounds
Preorder.toLE
mem_lowerBounds_iff_subset_Ici 📖mathematicalSet
Set.instMembership
lowerBounds
Preorder.toLE
Set.instHasSubset
Set.Ici
mem_upperBounds 📖mathematicalSet
Set.instMembership
upperBounds
Preorder.toLE
mem_upperBounds_iff_subset_Iic 📖mathematicalSet
Set.instMembership
upperBounds
Preorder.toLE
Set.instHasSubset
Set.Iic
minimal_iff_isLeast 📖mathematicalMinimal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
IsLeast
DirectedOn.minimal_iff_isLeast
Std.Total.directedOn
LE.total'
nonempty_of_not_bddAbove 📖mathematicalBddAbove
Preorder.toLE
Set.Nonemptynot_bddAbove_iff'
nonempty_of_not_bddBelow 📖mathematicalBddBelow
Preorder.toLE
Set.Nonemptynot_bddBelow_iff'
not_bddAbove_iff 📖mathematicalBddAbove
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Preorder.toLT
not_bddAbove_iff' 📖mathematicalBddAbove
Preorder.toLE
Set
Set.instMembership
not_bddAbove_univ 📖mathematicalBddAbove
Preorder.toLE
Set.univ
NoTopOrder.upperBounds_univ
not_bddBelow_iff 📖mathematicalBddBelow
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Preorder.toLT
not_bddBelow_iff'
not_le
not_bddBelow_iff' 📖mathematicalBddBelow
Preorder.toLE
Set
Set.instMembership
not_bddBelow_univ 📖mathematicalBddBelow
Preorder.toLE
Set.univ
NoBotOrder.lowerBounds_univ
Set.not_nonempty_empty
subset_lowerBounds_upperBounds 📖mathematicalSet
Set.instHasSubset
lowerBounds
Preorder.toLE
upperBounds
subset_upperBounds_lowerBounds 📖mathematicalSet
Set.instHasSubset
upperBounds
Preorder.toLE
lowerBounds
top_mem_upperBounds 📖mathematicalSet
Set.instMembership
upperBounds
Preorder.toLE
Top.top
OrderTop.toTop
le_top
union_lowerBounds_subset_lowerBounds_inter 📖mathematicalSet
Set.instHasSubset
Set.instUnion
lowerBounds
Preorder.toLE
Set.instInter
Set.union_subset
lowerBounds_mono_set
Set.inter_subset_left
Set.inter_subset_right
union_upperBounds_subset_upperBounds_inter 📖mathematicalSet
Set.instHasSubset
Set.instUnion
upperBounds
Preorder.toLE
Set.instInter
Set.union_subset
upperBounds_mono_set
Set.inter_subset_left
Set.inter_subset_right
upperBounds_Icc 📖mathematicalPreorder.toLEupperBounds
Set.Icc
Set.Ici
IsLUB.upperBounds_eq
isLUB_Icc
upperBounds_Ico 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
upperBounds
Preorder.toLE
Set.Ico
Set.Ici
IsLUB.upperBounds_eq
isLUB_Ico
upperBounds_Iic 📖mathematicalupperBounds
Preorder.toLE
Set.Iic
Set.Ici
IsLUB.upperBounds_eq
isLUB_Iic
upperBounds_Iio 📖mathematicalupperBounds
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Iio
Set.Ici
IsLUB.upperBounds_eq
isLUB_Iio
upperBounds_Ioc 📖mathematicalPreorder.toLTupperBounds
Preorder.toLE
Set.Ioc
Set.Ici
IsLUB.upperBounds_eq
isLUB_Ioc
upperBounds_Ioo 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
upperBounds
Preorder.toLE
Set.Ioo
Set.Ici
IsLUB.upperBounds_eq
isLUB_Ioo
upperBounds_empty 📖mathematicalupperBounds
Preorder.toLE
Set
Set.instEmptyCollection
Set.univ
upperBounds_insert 📖mathematicalupperBounds
Preorder.toLE
Set
Set.instInsert
Set.instInter
Set.Ici
Set.insert_eq
upperBounds_union
upperBounds_singleton
upperBounds_mono 📖Set
Set.instHasSubset
Preorder.toLE
Set.instMembership
upperBounds
upperBounds_mono_set
upperBounds_mono_mem
upperBounds_mono_mem 📖Preorder.toLE
Set
Set.instMembership
upperBounds
le_trans
upperBounds_mono_of_isCofinalFor 📖mathematicalIsCofinalFor
Preorder.toLE
Set
Set.instHasSubset
upperBounds
LE.le.trans
upperBounds_mono_set 📖mathematicalSet
Set.instHasSubset
upperBounds
Preorder.toLE
upperBounds_prod 📖mathematicalSet.NonemptyupperBounds
Prod.instLE_mathlib
Preorder.toLE
SProd.sprod
Set
Set.instSProd
Set.ext
Set.nonempty_coe_sort
upperBounds_singleton 📖mathematicalupperBounds
Preorder.toLE
Set
Set.instSingletonSet
Set.Ici
IsLUB.upperBounds_eq
isLUB_singleton
upperBounds_union 📖mathematicalupperBounds
Preorder.toLE
Set
Set.instUnion
Set.instInter
Set.Subset.antisymm

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