Documentation Verification Report

Monotone

πŸ“ Source: Mathlib/Topology/Order/Monotone.lean

Statistics

MetricCount
DefinitionsMonotone
1
Theoremscountable_not_continuousAt, countable_setOf_two_preimages, map_ciInf_of_continuousAt, map_ciSup_of_continuousAt, map_csInf_of_continuousAt, map_csSup_of_continuousAt, map_iInf_of_continuousAt, map_iSup_of_continuousAt, map_sInf_of_continuousAt, map_sSup_of_continuousAt, tendsto_nhdsGT, tendsto_nhdsLT, countable_not_continuousWithinAt, countable_setOf_two_preimages, map_csInf_of_continuousWithinAt, map_csSup_of_continuousWithinAt, map_sInf_of_continuousWithinAt, map_sSup_of_continuousWithinAt, tendsto_nhdsGT, tendsto_nhdsLT, tendsto_nhdsWithin_Ioo_left, tendsto_nhdsWithin_Ioo_right, csInf_mem, csSup_mem, isGreatest_csSup, isLeast_csInf, sInf_mem, sSup_mem, countable_not_continuousAt, countable_setOf_two_preimages, map_ciInf_of_continuousAt, map_ciSup_of_continuousAt, map_csInf_of_continuousAt, map_csSup_of_continuousAt, map_iInf_of_continuousAt, map_iSup_of_continuousAt, map_sInf_of_continuousAt, map_sSup_of_continuousAt, tendsto_nhdsGT, tendsto_nhdsLT, countable_not_continuousWithinAt, countable_not_continuousWithinAt_Iio, countable_not_continuousWithinAt_Ioi, countable_setOf_two_preimages, insert_of_continuousWithinAt, map_csInf_of_continuousWithinAt, map_csSup_of_continuousWithinAt, map_sInf_of_continuousWithinAt, map_sSup_of_continuousWithinAt, tendsto_nhdsGT, tendsto_nhdsLT, tendsto_nhdsWithin_Ioo_left, tendsto_nhdsWithin_Ioo_right, csInf_mem_closure, csSup_mem_closure, sInf_mem_closure, sSup_mem_closure
57
Total58

Antitone

Theorems

NameKindAssumesProvesValidatesDepends On
countable_not_continuousAt πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
ContinuousAt
β€”Monotone.countable_not_continuousAt
instOrderTopologyOrderDual
instSecondCountableTopologyOrderDual
dual_right
countable_setOf_two_preimages πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
Preorder.toLT
β€”Monotone.countable_setOf_two_preimages
dual_right
map_ciInf_of_continuousAt πŸ“–mathematicalContinuousAt
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Antitone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
BddBelow
Preorder.toLE
Set.range
iSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”iInf.eq_1
map_csInf_of_continuousAt
Set.range_nonempty
Set.range_comp
iSup.eq_1
map_ciSup_of_continuousAt πŸ“–mathematicalContinuousAt
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Antitone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
BddAbove
Preorder.toLE
Set.range
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”iSup.eq_1
map_csSup_of_continuousAt
Set.range_nonempty
Set.range_comp
iInf.eq_1
map_csInf_of_continuousAt πŸ“–mathematicalContinuousAt
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Antitone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Set.Nonempty
BddBelow
Preorder.toLE
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
Set.image
β€”Monotone.map_csInf_of_continuousAt
instOrderClosedTopologyOrderDual
dual_right
map_csSup_of_continuousAt πŸ“–mathematicalContinuousAt
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Antitone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Set.Nonempty
BddAbove
Preorder.toLE
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
Set.image
β€”Monotone.map_csSup_of_continuousAt
instOrderClosedTopologyOrderDual
dual_right
map_iInf_of_continuousAt πŸ“–mathematicalContinuousAt
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
Antitone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
CoheytingAlgebra.toOrderTop
Bot.bot
OrderBot.toBot
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
HeytingAlgebra.toOrderBot
iSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”Monotone.map_iInf_of_continuousAt
instOrderClosedTopologyOrderDual
map_iSup_of_continuousAt πŸ“–mathematicalContinuousAt
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
Antitone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
HeytingAlgebra.toOrderBot
Top.top
OrderTop.toTop
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CoheytingAlgebra.toOrderTop
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”Monotone.map_iSup_of_continuousAt
instOrderClosedTopologyOrderDual
map_sInf_of_continuousAt πŸ“–mathematicalContinuousAt
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
Antitone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
CoheytingAlgebra.toOrderTop
Bot.bot
OrderBot.toBot
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
HeytingAlgebra.toOrderBot
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
Set.image
β€”Monotone.map_sInf_of_continuousAt
instOrderClosedTopologyOrderDual
map_sSup_of_continuousAt πŸ“–mathematicalContinuousAt
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
Antitone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
HeytingAlgebra.toOrderBot
Top.top
OrderTop.toTop
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CoheytingAlgebra.toOrderTop
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
Set.image
β€”Monotone.map_sSup_of_continuousAt
instOrderClosedTopologyOrderDual
tendsto_nhdsGT πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Filter.Tendsto
nhdsWithin
Set.Ioi
nhds
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
Set.image
β€”Monotone.tendsto_nhdsGT
instOrderTopologyOrderDual
dual_right
tendsto_nhdsLT πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Filter.Tendsto
nhdsWithin
Set.Iio
nhds
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
Set.image
β€”Monotone.tendsto_nhdsLT
instOrderTopologyOrderDual
dual_right

AntitoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
countable_not_continuousWithinAt πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
Set
Set.instMembership
ContinuousWithinAt
β€”MonotoneOn.countable_not_continuousWithinAt
instOrderTopologyOrderDual
instSecondCountableTopologyOrderDual
dual_right
countable_setOf_two_preimages πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
Set
Set.instMembership
Preorder.toLT
β€”MonotoneOn.countable_setOf_two_preimages
dual_right
map_csInf_of_continuousWithinAt πŸ“–mathematicalContinuousWithinAt
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
AntitoneOn
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Set.Nonempty
BddBelow
Preorder.toLE
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
Set.image
β€”MonotoneOn.map_csInf_of_continuousWithinAt
instOrderClosedTopologyOrderDual
dual_right
map_csSup_of_continuousWithinAt πŸ“–mathematicalContinuousWithinAt
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
AntitoneOn
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Set.Nonempty
BddAbove
Preorder.toLE
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
Set.image
β€”MonotoneOn.map_csSup_of_continuousWithinAt
instOrderClosedTopologyOrderDual
dual_right
map_sInf_of_continuousWithinAt πŸ“–mathematicalContinuousWithinAt
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
AntitoneOn
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
CoheytingAlgebra.toOrderTop
Bot.bot
OrderBot.toBot
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
HeytingAlgebra.toOrderBot
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
Set.image
β€”MonotoneOn.map_sInf_of_continuousWithinAt
instOrderClosedTopologyOrderDual
map_sSup_of_continuousWithinAt πŸ“–mathematicalContinuousWithinAt
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
AntitoneOn
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
HeytingAlgebra.toOrderBot
Top.top
OrderTop.toTop
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CoheytingAlgebra.toOrderTop
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
Set.image
β€”MonotoneOn.map_sSup_of_continuousWithinAt
instOrderClosedTopologyOrderDual
tendsto_nhdsGT πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Set.Ioi
BddAbove
Preorder.toLE
Set.image
Filter.Tendsto
nhdsWithin
nhds
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”MonotoneOn.tendsto_nhdsGT
instOrderTopologyOrderDual
dual_right
tendsto_nhdsLT πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Set.Iio
BddBelow
Preorder.toLE
Set.image
Filter.Tendsto
nhdsWithin
nhds
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”MonotoneOn.tendsto_nhdsLT
instOrderTopologyOrderDual
dual_right
tendsto_nhdsWithin_Ioo_left πŸ“–mathematicalSet.Nonempty
Set.Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AntitoneOn
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
BddBelow
Preorder.toLE
Set.image
Filter.Tendsto
nhdsWithin
Set.Iio
nhds
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”MonotoneOn.tendsto_nhdsWithin_Ioo_left
instOrderTopologyOrderDual
dual_right
tendsto_nhdsWithin_Ioo_right πŸ“–mathematicalSet.Nonempty
Set.Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AntitoneOn
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
BddAbove
Preorder.toLE
Set.image
Filter.Tendsto
nhdsWithin
Set.Ioi
nhds
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”MonotoneOn.tendsto_nhdsWithin_Ioo_right
instOrderTopologyOrderDual
dual_right

IsClosed

Theorems

NameKindAssumesProvesValidatesDepends On
csInf_mem πŸ“–mathematicalSet.Nonempty
BddBelow
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Set
Set.instMembership
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”IsGLB.mem_of_isClosed
isGLB_csInf
csSup_mem πŸ“–mathematicalSet.Nonempty
BddAbove
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Set
Set.instMembership
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”IsLUB.mem_of_isClosed
isLUB_csSup
isGreatest_csSup πŸ“–mathematicalSet.Nonempty
BddAbove
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
IsGreatest
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”isLeast_csInf
instOrderTopologyOrderDual
isLeast_csInf πŸ“–mathematicalSet.Nonempty
BddBelow
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
IsLeast
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”csInf_mem
isGLB_csInf
sInf_mem πŸ“–mathematicalSet.NonemptySet
Set.instMembership
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
β€”IsGLB.mem_of_isClosed
isGLB_sInf
sSup_mem πŸ“–mathematicalSet.NonemptySet
Set.instMembership
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
β€”IsLUB.mem_of_isClosed
isLUB_sSup

Monotone

Theorems

NameKindAssumesProvesValidatesDepends On
countable_not_continuousAt πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
ContinuousAt
β€”MonotoneOn.countable_not_continuousWithinAt
monotoneOn
countable_setOf_two_preimages πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
Preorder.toLT
β€”MonotoneOn.countable_setOf_two_preimages
monotoneOn_univ
map_ciInf_of_continuousAt πŸ“–β€”ContinuousAt
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Monotone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
BddBelow
Preorder.toLE
Set.range
β€”β€”iInf.eq_1
map_csInf_of_continuousAt
Set.range_nonempty
Set.range_comp
map_ciSup_of_continuousAt πŸ“–β€”ContinuousAt
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Monotone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
BddAbove
Preorder.toLE
Set.range
β€”β€”iSup.eq_1
map_csSup_of_continuousAt
Set.range_nonempty
Set.range_comp
map_csInf_of_continuousAt πŸ“–mathematicalContinuousAt
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Monotone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Set.Nonempty
BddBelow
Preorder.toLE
Set.imageβ€”map_csSup_of_continuousAt
instOrderTopologyOrderDual
instOrderClosedTopologyOrderDual
dual
map_csSup_of_continuousAt πŸ“–mathematicalContinuousAt
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Monotone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Set.Nonempty
BddAbove
Preorder.toLE
Set.imageβ€”MonotoneOn.map_csSup_of_continuousWithinAt
ContinuousAt.continuousWithinAt
monotoneOn
map_iInf_of_continuousAt πŸ“–β€”ContinuousAt
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
Monotone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
CoheytingAlgebra.toOrderTop
β€”β€”map_iSup_of_continuousAt
instOrderTopologyOrderDual
instOrderClosedTopologyOrderDual
dual
map_iSup_of_continuousAt πŸ“–β€”ContinuousAt
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
Monotone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
HeytingAlgebra.toOrderBot
β€”β€”iSup.eq_1
map_sSup_of_continuousAt
Set.range_comp
map_sInf_of_continuousAt πŸ“–mathematicalContinuousAt
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
Monotone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
CoheytingAlgebra.toOrderTop
Set.imageβ€”map_sSup_of_continuousAt
instOrderTopologyOrderDual
instOrderClosedTopologyOrderDual
dual
map_sSup_of_continuousAt πŸ“–mathematicalContinuousAt
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
Monotone
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
HeytingAlgebra.toOrderBot
Set.imageβ€”MonotoneOn.map_sSup_of_continuousWithinAt
ContinuousAt.continuousWithinAt
monotoneOn
tendsto_nhdsGT πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Filter.Tendsto
nhdsWithin
Set.Ioi
nhds
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
Set.image
β€”tendsto_nhdsLT
instOrderTopologyOrderDual
dual
tendsto_nhdsLT πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Filter.Tendsto
nhdsWithin
Set.Iio
nhds
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
Set.image
β€”MonotoneOn.tendsto_nhdsLT
monotoneOn
map_bddAbove
bddAbove_Iio

MonotoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
countable_not_continuousWithinAt πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
Set
Set.instMembership
ContinuousWithinAt
β€”Set.Countable.mono
Set.Countable.union
countable_not_continuousWithinAt_Ioi
countable_not_continuousWithinAt_Iio
Set.compl_subset_compl
Set.compl_union
continuousWithinAt_iff_continuous_left'_right'
countable_not_continuousWithinAt_Iio πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
Set
Set.instMembership
ContinuousWithinAt
Set.instInter
Set.Iio
β€”countable_not_continuousWithinAt_Ioi
instOrderTopologyOrderDual
instSecondCountableTopologyOrderDual
dual
countable_not_continuousWithinAt_Ioi πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
Set
Set.instMembership
ContinuousWithinAt
Set.instInter
Set.Ioi
β€”Set.Countable.mono
countable_image_lt_image_Ioi_within
Mathlib.Tactic.Contrapose.contraposeβ‚‚
Mathlib.Tactic.Push.not_and_eq
Mathlib.Tactic.Push.not_forall_eq
tendsto_order
Filter.mp_mem
self_mem_nhdsWithin
Filter.univ_mem'
LT.lt.trans_le
le_of_lt
nhdsWithin_inter
Ioo_mem_nhdsGT
instClosedIciTopology
OrderTopology.to_orderClosedTopology
LE.le.trans_lt
LT.lt.le
countable_setOf_two_preimages πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Countable
setOf
Set
Set.instMembership
Preorder.toLT
β€”Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim
Set.PairwiseDisjoint.countable_of_Ioo
LT.lt.le
LT.lt.trans
not_le
Disjoint.symm
le_antisymm
le_trans
le_refl
le_of_not_gt
Set.countable_of_injective_of_countable_image
Nontrivial.to_nonempty
Function.sometimes_spec
insert_of_continuousWithinAt πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ContinuousWithinAt
Set
Set.instInsert
β€”Set.monotoneOn_insert_iff
LE.le.eq_or_lt
le_rfl
ge_of_tendsto
instClosedIciTopology
inter_mem_nhdsWithin
Ioi_mem_nhds
instClosedIicTopology
OrderTopology.to_orderClosedTopology
Filter.mp_mem
Filter.univ_mem'
le_of_lt
le_of_tendsto
Iio_mem_nhds
map_csInf_of_continuousWithinAt πŸ“–mathematicalContinuousWithinAt
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
MonotoneOn
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Set.Nonempty
BddBelow
Preorder.toLE
Set.imageβ€”map_csSup_of_continuousWithinAt
instOrderTopologyOrderDual
instOrderClosedTopologyOrderDual
dual
map_csSup_of_continuousWithinAt πŸ“–mathematicalContinuousWithinAt
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
MonotoneOn
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Set.Nonempty
BddAbove
Preorder.toLE
Set.imageβ€”IsLUB.csSup_eq
IsLUB.isLUB_of_tendsto
isLUB_csSup
Filter.Tendsto.mono_left
Set.Nonempty.image
map_sInf_of_continuousWithinAt πŸ“–mathematicalContinuousWithinAt
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
MonotoneOn
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
CompleteDistribLattice.toCoframe
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
CoheytingAlgebra.toOrderTop
Set.imageβ€”map_sSup_of_continuousWithinAt
instOrderTopologyOrderDual
instOrderClosedTopologyOrderDual
dual
map_sSup_of_continuousWithinAt πŸ“–mathematicalContinuousWithinAt
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
MonotoneOn
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompletelyDistribLattice.toCompleteDistribLattice
CompleteLinearOrder.toCompletelyDistribLattice
HeytingAlgebra.toOrderBot
Set.imageβ€”Set.eq_empty_or_nonempty
sSup_empty
Set.image_empty
map_csSup_of_continuousWithinAt
OrderTop.bddAbove
tendsto_nhdsGT πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Set.Ioi
BddBelow
Preorder.toLE
Set.image
Filter.Tendsto
nhdsWithin
nhds
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”tendsto_nhdsLT
instOrderTopologyOrderDual
dual
tendsto_nhdsLT πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Set.Iio
BddAbove
Preorder.toLE
Set.image
Filter.Tendsto
nhdsWithin
nhds
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”Set.eq_empty_or_nonempty
nhdsWithin_empty
Set.image_empty
tendsto_order
exists_lt_of_lt_csSup
Set.Nonempty.image
Filter.mp_mem
Ioo_mem_nhdsLT
instClosedIicTopology
OrderTopology.to_orderClosedTopology
Filter.univ_mem'
LT.lt.trans_le
LT.lt.le
Filter.mem_of_superset
self_mem_nhdsWithin
lt_of_le_of_lt
le_csSup
Set.mem_image_of_mem
tendsto_nhdsWithin_Ioo_left πŸ“–mathematicalSet.Nonempty
Set.Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MonotoneOn
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
BddAbove
Preorder.toLE
Set.image
Filter.Tendsto
nhdsWithin
Set.Iio
nhds
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”tendsto_order
exists_lt_of_lt_csSup
Set.Nonempty.image
Filter.mp_mem
Ioo_mem_nhdsLT
instClosedIicTopology
OrderTopology.to_orderClosedTopology
Filter.univ_mem'
LT.lt.trans_le
LT.lt.le
LT.lt.trans
LE.le.trans_lt
le_csSup
Set.mem_image_of_mem
tendsto_nhdsWithin_Ioo_right πŸ“–mathematicalSet.Nonempty
Set.Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MonotoneOn
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
BddBelow
Preorder.toLE
Set.image
Filter.Tendsto
nhdsWithin
Set.Ioi
nhds
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”tendsto_order
Filter.mp_mem
Ioo_mem_nhdsGT
instClosedIciTopology
OrderTopology.to_orderClosedTopology
LT.lt.trans
Filter.univ_mem'
LT.lt.trans_le
csInf_le
Set.mem_image_of_mem
exists_lt_of_csInf_lt
Set.Nonempty.image
LE.le.trans_lt
LT.lt.le

(root)

Definitions

NameCategoryTheorems
Monotone πŸ“–MathDef
582 mathmath: Pi.single_mono, Finset.toLeft_monotone, Dynamics.netEntropyEntourage_monotone, oneLePart_mono, NonemptyInterval.toDualProd_mono, Dynamics.netMaxcard_monotone_subset, Set.ncard_mono, Submonoid.monotone_comap, Set.IsPWO.exists_monotone_subseq, PositiveLinearMap.monotone', GaloisConnection.monotone_u, toAntisymmetrization_mono, NonUnitalSubring.toAddSubgroup_mono, OrdinalApprox.lfpApprox_mono_mid, Finset.sum_mono_set, not_monotone_not_antitone_iff_exists_le_le, MeasureTheory.hittingBtwn_apply_mono_right, Order.sequenceOfCofinals.monotone, MeasureTheory.hittingBtwn_mono_left, CategoryTheory.Sieve.generate_mono, WithTop.coe_mono, Nucleus.monotone, monotone_fst, partialSups_mono, CFC.monotone_nnrpow, FirstOrder.Language.PartialEquiv.monotone_symm, Fin.predAbove_left_monotone, MonotoneOn.Iic_union_Ici, Nat.succPNat_mono, Function.monotone_eval, OrderEmbedding.monotone, Real.monotone_rpow_of_base_ge_one, Finsupp.toColex_monotone, Antitone.const_mul_of_nonpos, exists_monotone_Icc_subset_open_cover_Icc, Filter.map_mono, Pi.toColex_monotone, Function.update_mono, Submodule.restrictScalars_monotone, Matroid.eRk_mono, Antitone.neg, monotone_hausdorffEntourage, MeasureTheory.monotone_spanningSets, OrderIso.monotone, Valuation.leSubmodule_monotone, ENNReal.monotone_rpow_of_nonneg, AddSubgroup.prod_mono_left, monotone_transfiniteIterate, DFinsupp.coe_mono, Nat.nth_monotone, nsmul_right_mono, Finset.subtype_mono, upperCentralSeries_mono, monotone_of_deriv_nonneg, SetRel.core_mono, Nat.monotone_primeCounting', IsFiltration.mono, CategoryTheory.Sieve.pullback_monotone, DFinsupp.toLex_monotone, Quotient.mk_monotone, Topology.IsUpperSet.monotone_iff_continuous, Antitone.dual_right, MeasureTheory.Measure.LebesgueDecomposition.iSup_monotone, OrderHom.monotone, Order.pred_le_pred_of_le, Finset.monotone_iff_forall_le_cons, Cardinal.mk_monotone, ENat.monotone_map_iff, Subring.toAddSubgroup_mono, CategoryTheory.GrothendieckTopology.monotone_close, MeasureTheory.hittingAfter_mono, LinearEquiv.dilatransvections_pow_mono, StrictMono.monotone, monotone_const, Subgroup.toSubmonoid_mono, InitialSeg.monotone, Subsemiring.homogeneousCore_mono, Real.monotone_arcsin, StieltjesFunction.mono', Prod.Lex.monotone_fst_ofLex, CategoryTheory.MorphismProperty.monotone_map, BoxIntegral.Box.monotone_face, MonoidWithZeroHom.fst_mono, NNRat.cast_mono, Antivary.exists_antitone_monotone, ProbabilityTheory.monotone_cdf, UniformFun.mono, monotone_dual_iff, Cardinal.ofENat_mono, Valuation.ltAddSubgroup_monotone, Order.pred_mono, AlgebraicGeometry.Scheme.IdealSheafData.comap_mono, Finset.pow_right_monotone, monotone_add_nat_iff_monotoneOn_nat_Ici, monotone_add_nat_of_le_succ, ScottContinuousOn.monotone, Set.monotone_projIic, Order.IsNormal.monotone, Monotone.of_map_inf_le_left, monotone_prod_iff, Subring.toSubmonoid_mono, Monotone.of_map_inf, monotone_smul_right_of_nonneg, Subring.toSubsemiring_mono, Tuple.monotone_proj, Finset.monotone_iff_forall_le_insert, Dynamics.coverEntropy_monotone, CategoryTheory.MorphismProperty.coproducts_monotone, Module.Basis.flag_mono, eVariationOn.nonempty_monotone_mem, Dynamics.coverMincard_monotone_time, MonoidHom.inr_mono, Fintype.prod_mono', Real.sqrt_monotone, OrderMonoidWithZeroHom.monotone', StrictMono.trans_monovary, Cardinal.lift_monotone, monotone_vecEmpty, CategoryTheory.MorphismProperty.multiplicativeClosure_monotone, Nat.mono_cast, latticeClosure_mono, Nat.ceil_mono, Tuple.sort_eq_refl_iff_monotone, MeasureTheory.hittingBtwn_mono, FractionalIdeal.mul_right_mono, LocalSubring.toSubring_mono, RCLike.re_monotone, Fintype.sum_mono, WithBot.monotone_map_iff, WithTop.monotone_map_iff, ProbabilityTheory.monotone_defaultRatCDF, Besicovitch.TauPackage.monotone_iUnionUpTo, CategoryTheory.Triangulated.TStructure.le_monotone, Antitone.comp, Real.exp_monotone, IsOpen.exists_iUnion_isClosed, Real.toNNReal_monotone, Matroid.cRk_mono, Urysohns.CU.approx_mono, Finset.nsmul_right_monotone, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_monotone, antitone_toDual_comp_iff, Subsemiring.prod_mono_right, Sum.Lex.inl_mono, PrincipalSeg.monotone, PNat.natPred_monotone, Nat.choose_mono, Subalgebra.separatesPoints_monotone, RingPreordering.toSubsemiring_mono, monotone_id, RightOrdContinuous.mono, Nat.fib_mono, monotone_mul_right_of_nonneg, Filter.monotone_mem, Int.floor_mono, Matroid.closure_mono, Topology.IsLowerSet.monotone_iff_continuous, Set.offDiag_mono, WithBot.succ_mono, monotone_prodMk_iff, partialSups_monotone, Finset.offDiag_mono, LieSubmodule.monotone_normalizer, monotone_smul_left_of_nonneg, ProbabilityTheory.IsRatCondKernelCDFAux.mono, Nat.clog_monotone, Subsemiring.toSubmonoid_mono, Submodule.toAddSubgroup_mono, Set.monotoneOn_iff_monotone, AffineMap.lineMap_mono, ExpGrowth.expGrowthInf_monotone, SSet.Subcomplex.image_monotone, ENat.epow_right_mono, algebraMap_monotone, smul_mono_right, Set.kernImage_mono, monotone_iff_forall_lt', Set.monotone_accumulate, monotone_iff_map_nonneg, AddSubmonoid.addUnits_mono, CategoryTheory.Functor.monotone, Finsupp.mapDomain_mono, Digraph.toSimpleGraphStrict_mono, monotone_toDual_comp_iff, mul_right_mono, zsmul_mono_right, EReal.exp_monotone, OrderAddMonoidHom.monotone', CircleDeg1Lift.iterate_monotone, pow_left_mono, Finset.Nonempty.card_nsmul_mono, ENNReal.log_monotone, NonUnitalSubalgebra.starClosure_mono, List.SortedLE.monotone_get, Filter.comap_mono, Submodule.toAddSubmonoid_mono, NonUnitalSubsemiring.toAddSubmonoid_mono, AddMonoidHom.snd_mono, exists_seq_tendsto_sSup, Subring.prod_mono_left, Set.nsmul_right_monotone, List.SortedLE.monotone, EReal.monotone_div_right_of_nonneg, LieIdeal.map_mono, Dynamics.coverEntropyEntourage_monotone, BooleanSubalgebra.comap_mono, AlgebraicGeometry.Scheme.IdealSheafData.ofIdeals_mono, NNReal.agmSequences_fst_monotone, Cardinal.beth_mono, OrderHomClass.mono, antivary_iff_exists_monotone_antitone, List.Sorted.get_mono, MeasureTheory.hittingBtwn_apply_mono_left, Finsupp.coe_strictMono, Cardinal.powerlt_mono_left, OrdinalApprox.lfpApprox_monotone, Finset.disjSum_mono_right, DyckWord.monotone_semilength, Fin.predAbove_right_monotone, ProbabilityTheory.monotone_preCDF, AddMonoidHom.inr_mono, WithBot.monotone_iff, Dynamics.coverEntropyInf_monotone, WithTop.pred_mono, FirstOrder.Language.HomClass.monotone, ack_mono_right, AlgebraicGeometry.Scheme.IdealSheafData.map_mono, CFC.monotone_rpow, ENNReal.monotone_truncateToReal, Multiset.disjSum_mono_right, SimpleGraph.Subgraph.verts_monotone, Finset.toRight_monotone, Subtype.mono_coe, Nat.count_monotone, Set.isPWO_iff_exists_monotone_subseq, Sublattice.prod_left_mono, ValuationSubring.monotone_mapOfLE, NonUnitalSubring.prod_mono_left, CategoryTheory.Sieve.functorPushforward_monotone, LeftOrdContinuous.mono, Valuation.ltSubmodule_monotone, exists_monotone_Icc_subset_open_cover_unitInterval_prod_self, Finsupp.single_mono, MonomialOrder.toSyn_monotone, Antitone.Ioi, Finset.monotone_filter_left, StieltjesFunction.mono, monotone_int_of_le_succ, Sum.inl_mono, Set.monotone_or_antitone_iff_uIcc, monotone_of_le_add_one, Set.pow_right_monotone, OrderHom.canLift, Ideal.homogeneousHull_mono, Order.pred_le_pred_of_not_isMin_of_le, Dynamics.netEntropyInfEntourage_monotone, monotone_iff_map_nonpos, OrderHomClass.monotone, Sublattice.comap_mono, Chebyshev.theta_mono, Antitone.Ici, List.monotone_sum_take, LinearEquiv.transvections_pow_mono, MonoidHom.inl_mono, Ordinal.IsNormal.monotone, ProbabilityTheory.IsRatStieltjesPoint.mono, Subsemigroup.monotone_comap, MeasureTheory.OuterMeasure.comap_mono, CauchyFilter.monotone_gen, Set.monotone_mem, AddConstMapClass.monotone_iff_Icc, mul_left_mono, ENat.toENNReal_mono, ENat.floor_mono, MeasureTheory.Measure.LebesgueDecomposition.iSup_monotone', MonoidWithZeroHom.inr_mono, grade_mono, AddSubgroup.ofAddUnits_mono, NonUnitalSubsemiring.prod_mono_left, ENat.epow_left_mono, LinearOrderedField.inducedMap_mono, BoxIntegral.Box.monotone_upper, AddMonoidHom.inl_mono, CategoryTheory.Sieve.functorPullback_monotone, Subgroup.ofUnits_mono, Tuple.comp_sort_eq_comp_iff_monotone, Finset.Colex.toColex_mono, Covariant.monotone_of_const, Subsemigroup.monotone_map, pow_right_monotone, zpow_left_mono, Set.encard_mono, OrdinalApprox.lfpApprox_mono_left, FirstOrder.Language.PartialEquiv.monotone_cod, MeasureTheory.hittingBtwn_mono_right, monotone_Iio, Nat.monotone_factorial, SSet.stdSimplex.monotone_apply, Dynamics.netMaxcard_monotone_time, FirstOrder.Language.monotone_distinctConstantsTheory, MeasureTheory.SimpleFunc.monotone_eapprox, Subsingleton.monotone, Topology.IsScott.monotone_of_continuous, Real.sigmoid_monotone, Rat.cast_mono, List.sorted_le_ofFn_iff, StarSubalgebra.topologicalClosure_mono, SetRel.image_mono, OrderHom.mono, Multiset.map_mono, FractionalIdeal.mul_left_mono, NNReal.agmSequences_monotone_and_antitone, LowerAdjoint.monotone, Finset.Nonempty.card_pow_mono, isClosed_monotone, SimpleGraph.map_monotone, NonUnitalSubsemiring.toSubsemigroup_mono, UniformSpace.comap_mono, supClosure_mono, nsmul_left_monotone, NNRat.toNNRat_mono, monotone_iff_forall_wcovBy, Multiset.card_mono, MeasureTheory.OuterMeasure.mkMetric'.mono_pre_nat, Digraph.toSimpleGraphInclusive_mono, MeasureTheory.monotone_lintegral, Antitone.dual_left, FirstOrder.Language.Substructure.monotone_map, Tuple.eq_sort_iff, monovary_id_iff, BooleanSubalgebra.map_mono, Projectivization.Subspace.monotone_span, Valuation.leIdeal_mono, OrderRingHom.monotone', monotone_Iic, SimpleGraph.Subgraph.map_monotone, List.monotone_prod_take, SetRel.preimage_mono, Finset.upShadow_monotone, Order.succ_mono, Nat.monotone_primeCounting, SimplexCategory.II.monotone_map', Sublattice.prod_right_mono, pow_right_mono₀, expNegInvGlue.monotone, Filter.exists_seq_monotone_tendsto_atTop_atTop, WithBotTop.coe_monotone, Finset.dens_mono, MeasureTheory.hitting_mono, MonoidWithZeroHom.snd_mono, monotone_le, OmegaCompletePartialOrder.ContinuousHom.monotone, Subgroup.prod_mono_left, monotone_of_odd_of_monotoneOn_nonneg, Filter.ker_mono, LieIdeal.comap_mono, OrdinalApprox.gfpApprox_mono_mid, MonotoneOn.monotone, NNReal.coe_mono, Finset.prod_mono_set', ENat.ceil_mono, OrderMonoidHom.monotone', NonUnitalSubring.toSubsemigroup_mono, MonoidHom.fst_mono, NonUnitalSubalgebra.star_mono, Pi.one_mono, PadicInt.appr_mono, monotone_iff_forall_covBy, Int.cast_mono, Set.monotone_projIcc, AddSubsemigroup.monotone_comap, OmegaCompletePartialOrder.ωScottContinuous.monotone, Function.const_mono, AddMonoidHom.fst_mono, NNReal.monotone_nnrpow_const, Tropical.untrop_monotone, Multiset.monotone_filter_left, Prod.Lex.toLex_mono, kstar_mono, BoxIntegral.Prepartition.monotone_restrict, Finset.monotone_sym2, NNRat.coe_mono, monotone_of_hasDerivAt_nonneg, Topology.RelCWComplex.skeleton_monotone, DFinsupp.coe_strictMono, Filter.monotone_smallSets, Filter.monotone_nhds, IsOrderRightAdjoint.right_mono, Submonoid.monotone_map, posTangentConeAt_mono, Monovary.exists_monotone, AlgebraicGeometry.Scheme.AffineZariskiSite.toOpens_mono, Composition.monotone_sizeUpTo, Subsingleton.monotone', Subsemiring.toAddSubmonoid_mono, monotone_div_right_of_nonneg, isUpperSet_setOf, TopologicalSpace.IrreducibleCloseds.map_mono, monotone_iff_apply₂, MeasurableSpace.generateMeasurableRec_mono, AddSubgroup.prod_mono_right, CFC.monotone_sqrt, OrdinalApprox.gfpApprox_mono_left, Set.monotone_preimage, CircleDeg1Lift.monotone, WithBot.coe_mono, MeasureTheory.OuterMeasure.trim_mono, Sublattice.map_mono, NNReal.monotone_rpow_of_nonneg, Finset.shadow_monotone, Subsemiring.prod_mono_left, Set.Icc.monotone_addNSMul, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mono, zpow_right_mono, DFinsupp.toColex_monotone, add_left_mono, ENNReal.monotone_zpow, CStarAlgebra.pow_monotone, Finset.diag_mono, ContinuousOrderHomClass.map_monotone, infClosure_mono, Antitone.mul, TwoSidedIdeal.matrix_monotone, monotone_iff_forall_lt, Antitone.mul_const_of_nonpos, monotone_of_pred_le, unitInterval.sigmoid_monotone, Ideal.homogeneousCore'_mono, monotone_snd, NonemptyInterval.toLex_mono, monotone_nhdsSet, ENNReal.coe_mono, Finset.disjSum_mono_left, CircleDeg1Lift.pow_monotone, WithTop.monotone_iff, Monotone.of_le_map_sup, Nat.floor_mono, MeasureTheory.hittingAfter_apply_mono, Real.arctan_mono, Sum.Lex.inr_mono, FirstOrder.Language.PartialEquiv.monotone_dom, Cycle.chain_mono, Ordinal.toZFSet_monotone, exists_monotone_Icc_subset_open_cover_unitInterval, monotone_lt, ClosureOperator.monotone, algebraMap_mono, zpow_right_mono₀, NonUnitalSubsemiring.prod_mono_right, posPart_mono, Finset.range_mono, FirstOrder.Language.Substructure.monotone_comap, MonoidWithZeroHom.inl_mono, antitone_comp_ofDual_iff, Int.ceil_mono, Subgroup.prod_mono_right, ProbabilityTheory.IsMeasurableRatCDF.monotone_stieltjesFunctionAux, IsLUB.exists_seq_monotone_tendsto, CategoryTheory.MorphismProperty.monotone_isoClosure, Order.height_mono, Finset.sum_mono_set_of_nonneg, CategoryTheory.Limits.IsFiltered.sequentialFunctor_map, Cardinal.preBeth_mono, Finset.image_mono, Finsupp.support_monotone, Submodule.span_monotone, SimpleGraph.Subgraph.comap_monotone, Ideal.homogeneousCore_mono, SimplexCategoryGenRel.simplicialEvalσ_monotone, Function.monotone_iterate_of_id_le, SzemerediRegularity.stepBound_mono, monotone_comp_ofDual_iff, Finsupp.degree_mono, AddSubsemigroup.monotone_map, Set.monotone_image, List.sortedLE_ofFn_iff, CompactlySupportedContinuousMap.monotone_of_nnreal, Ideal.matrix_monotone, add_right_mono, GaloisConnection.monotone_l, Valuation.ltIdeal_mono, Complex.monotone_ofReal, Finsupp.toLex_monotone, Real.smoothTransition.monotone, AddSubmonoid.monotone_comap, CategoryTheory.MorphismProperty.pullbacks_monotone, nhdsKer_mono, ringHom_monotone, StrictAnti.trans_antivary, monotone_of_le_succ, CategoryTheory.MorphismProperty.universally_mono, Equiv.Perm.monotone_iff, Finsupp.DegLex.monotone_degree, not_monotone_not_antitone_iff_exists_lt_lt, ProbabilityTheory.IsRatCondKernelCDF.mono, CategoryTheory.Sieve.pushforward_monotone, Topology.RelCWComplex.skeletonLT_monotone, Finsupp.coe_mono, monotone_of_sub_one_le, Valuation.leAddSubgroup_monotone, MeasureTheory.upcrossingsBefore_mono, NonUnitalSubring.prod_mono_right, Antitone.inv, monotone_mul_left_of_nonneg, Chebyshev.psi_mono, List.sortedLE_iff_monotone_get, Subalgebra.star_mono, Finset.monotone_preimage, MonoidHom.snd_mono, minSmoothness_monotone, Cardinal.ord_mono, MonotoneOn.exists_monotone_extension, Monotone.of_map_sup, monotone_vecCons, Pi.zero_mono, Nat.pow_self_mono, CategoryTheory.MorphismProperty.pushouts_monotone, Nat.fermatNumber_mono, Antivary.exists_monotone_antitone, Monotone.of_map_inf_le, ack_mono_left, Monotone.of_left_le_map_sup, MeasureTheory.Filtration.mono', CategoryTheory.MorphismProperty.retracts_monotone, MeasureTheory.SimpleFunc.monotone_approx, Continuous.specialization_monotone, monotoneOn_univ, Tropical.trop_monotone, Nat.greatestFib_mono, Pi.mulSingle_mono, RingCon.matrix_monotone, Submonoid.units_mono, ExpGrowth.expGrowthSup_monotone, gronwallBound_mono, Dynamics.coverEntropyInfEntourage_monotone, NonUnitalSubring.toNonUnitalSubsemiring_mono, Subgroup.IsSubnormal.isSubnormal_iff, ENNReal.ofReal_mono, Set.monotone_powerset, CircleDeg1Lift.translationNumber_mono, zsmul_left_mono, lowerClosure_mono, MeasurableSpace.monotone_map, AddSubmonoid.monotone_map, Finset.card_mono, Sum.inr_mono, Sum.Lex.toLex_mono, SetLike.coe_mono, CategoryTheory.MorphismProperty.transfiniteCompositions_monotone, Multiset.monotone_sym2, Subring.prod_mono_right, Set.monotone_projIci, MeasureTheory.OuterMeasure.map_mono, antivary_iff_exists_antitone_monotone, ruzsaSzemerediNumberNat_mono, Directed.sequence_mono, Ordinal.veblenWith_left_monotone, monovary_iff_exists_monotone, Submodule.toSubMulAction_mono, Tuple.monotone_sort, MeasurableSpace.monotone_comap, Dynamics.dynEntourage_monotone, Nat.log_monotone, DFinsupp.support_monotone, monotone_closure, Fin.monotone_iff_le_succ, Ordinal.monotone_gamma, AddSubgroup.IsSubnormal.isSubnormal_iff, ScottContinuous.monotone, Filter.monotone_principal, LTSeries.monotone, Multiset.disjSum_mono_left, Subgroup.IsSubnormal.exists_chain, Behrend.map_monotone, SimpleGraph.comap_monotone, Finset.prod_mono_set_of_one_le', AddSubgroup.toAddSubmonoid_mono, OrderHom.monotone', monotone_nat_of_le_succ, Pi.toLex_monotone, Dynamics.coverMincard_monotone_subset, Ordinal.veblen_left_monotone

Theorems

NameKindAssumesProvesValidatesDepends On
csInf_mem_closure πŸ“–mathematicalSet.Nonempty
BddBelow
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Set
Set.instMembership
closure
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”IsGLB.mem_closure
isGLB_csInf
csSup_mem_closure πŸ“–mathematicalSet.Nonempty
BddAbove
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
Set
Set.instMembership
closure
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
β€”IsLUB.mem_closure
isLUB_csSup
sInf_mem_closure πŸ“–mathematicalSet.NonemptySet
Set.instMembership
closure
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
β€”IsGLB.mem_closure
isGLB_sInf
sSup_mem_closure πŸ“–mathematicalSet.NonemptySet
Set.instMembership
closure
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
β€”IsLUB.mem_closure
isLUB_sSup

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