Documentation Verification Report

UnorderedInterval

πŸ“ Source: Mathlib/Order/Interval/Set/UnorderedInterval.lean

Statistics

MetricCount
DefinitionstermΞ™, Β«term[[_,_]]Β», uIcc, uIoc, uIoo
5
Theoremsimage_uIcc_subset, mapsTo_uIcc, image_uIcc_subset, mapsTo_uIcc, image_uIcc_subset, mapsTo_uIcc, image_uIcc_subset, mapsTo_uIcc, Icc_min_max, Icc_subset_uIcc, Icc_subset_uIcc', Ioc_subset_uIoc, Ioc_subset_uIoc', Ioo_min_max, Ioo_subset_uIoo, Ioo_subset_uIoo', bdd_below_bdd_above_iff_subset_uIcc, eq_of_mem_uIcc_of_mem_uIcc, eq_of_mem_uIcc_of_mem_uIcc', eq_of_mem_uIoc_of_mem_uIoc, eq_of_mem_uIoc_of_mem_uIoc', eq_of_notMem_uIoc_of_notMem_uIoc, forall_uIoc_iff, left_mem_uIcc, left_mem_uIoc, left_notMem_uIoo, mem_uIcc, mem_uIcc_of_ge, mem_uIcc_of_le, mem_uIoc, mem_uIoo_of_gt, mem_uIoo_of_lt, monotoneOn_or_antitoneOn_iff_uIcc, monotone_or_antitone_iff_uIcc, nonempty_uIcc, nonempty_uIoc, nonempty_uIoo, notMem_uIcc_of_gt, notMem_uIcc_of_lt, notMem_uIoc, right_mem_uIcc, right_mem_uIoc, right_notMem_uIoo, uIcc_comm, uIcc_eq_union, uIcc_injective_left, uIcc_injective_right, uIcc_ofDual, uIcc_of_ge, uIcc_of_gt, uIcc_of_le, uIcc_of_lt, uIcc_of_not_ge, uIcc_of_not_le, uIcc_prod_eq, uIcc_prod_uIcc, uIcc_self, uIcc_subset_Icc, uIcc_subset_uIcc, uIcc_subset_uIcc_iff_le, uIcc_subset_uIcc_iff_le', uIcc_subset_uIcc_iff_mem, uIcc_subset_uIcc_left, uIcc_subset_uIcc_right, uIcc_subset_uIcc_union_uIcc, uIcc_toDual, uIoc_comm, uIoc_eq_union, uIoc_injective_left, uIoc_injective_right, uIoc_of_ge, uIoc_of_le, uIoc_subset_uIcc, uIoc_subset_uIoc_of_uIcc_subset_uIcc, uIoc_union_uIoc, uIoo_comm, uIoo_eq_union, uIoo_ofDual, uIoo_of_ge, uIoo_of_gt, uIoo_of_le, uIoo_of_lt, uIoo_of_not_ge, uIoo_of_not_le, uIoo_self, uIoo_subset_Ioo, uIoo_subset_uIcc, uIoo_subset_uIcc_self, uIoo_toDual
89
Total94

Antitone

Theorems

NameKindAssumesProvesValidatesDepends On
image_uIcc_subset πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instHasSubset
Set.image
Set.uIcc
β€”AntitoneOn.image_uIcc_subset
antitoneOn
mapsTo_uIcc πŸ“–mathematicalAntitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.MapsTo
Set.uIcc
β€”AntitoneOn.mapsTo_uIcc
antitoneOn

AntitoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
image_uIcc_subset πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.uIcc
Set
Set.instHasSubset
Set.image
β€”Set.MapsTo.image_subset
mapsTo_uIcc
mapsTo_uIcc πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.uIcc
Set.MapsToβ€”Set.uIcc.eq_1
map_sup
Set.left_mem_uIcc
Set.right_mem_uIcc
map_inf
mapsTo_Icc

Interval

Definitions

NameCategoryTheorems
termΞ™ πŸ“–CompOpβ€”
Β«term[[_,_]]Β» πŸ“–CompOpβ€”

Monotone

Theorems

NameKindAssumesProvesValidatesDepends On
image_uIcc_subset πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instHasSubset
Set.image
Set.uIcc
β€”MonotoneOn.image_uIcc_subset
monotoneOn
mapsTo_uIcc πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.MapsTo
Set.uIcc
β€”MonotoneOn.mapsTo_uIcc
monotoneOn

MonotoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
image_uIcc_subset πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.uIcc
Set
Set.instHasSubset
Set.image
β€”Set.MapsTo.image_subset
mapsTo_uIcc
mapsTo_uIcc πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.uIcc
Set.MapsToβ€”Set.uIcc.eq_1
map_sup
Set.left_mem_uIcc
Set.right_mem_uIcc
map_inf
mapsTo_Icc

Set

Definitions

NameCategoryTheorems
uIcc πŸ“–CompOp
143 mathmath: Complex.verticalSegment_eq, Fin.image_castSucc_uIcc, Complex.norm_circleTransformBoundingFunction_le, Fin.preimage_addNat_uIcc_addNat, uIcc_injective_left, intervalIntegrable_iff', Antitone.mapsTo_uIcc, OrdConnected.uIcc_subset, image_single_uIcc_right, image_const_mul_uIcc, Icc_min_max, Filter.Tendsto.uIcc, ordConnected_iff_uIcc_subset_left, Path.range_subpathAux, uIcc_subset_uIcc_iff_mem, NNReal.segment_eq_uIcc, finite_uIcc, nhdsWithin_uIcc_isMeasurablyGenerated, neg_uIcc, segment_eq_uIcc, uIcc_of_lt, image_mulSingle_uIcc_left, uIcc_of_not_ge, mem_uIcc_of_le, AbsolutelyContinuousOnInterval.boundedVariationOn, Nonneg.segment_eq_uIcc, closure_uIoo, uIcc_comm, preimage_add_const_uIcc, strictConvex_uIcc, Icc_subset_uIcc, uIcc_prod_uIcc, notMem_uIcc_of_lt, uIcc_of_ge, uIcc_injective_right, NNReal.image_coe_uIcc, uIcc_of_le, Function.Periodic.image_uIcc, image_neg_uIcc, preimage_mul_const_uIcc, isCompact_uIcc, ncard_uIcc_nat, image_div_const_uIcc, unitInterval.volume_uIcc, closure_uIoc, Antitone.image_uIcc_subset, Fin.preimage_val_uIcc_val, intervalIntegral.FTCFilter.nhdsUIcc, Fin.preimage_castSucc_uIcc_castSucc, notMem_uIcc_of_gt, image_mulSingle_uIcc, Fin.preimage_succ_uIcc_succ, intervalIntegrable_sub_inv_iff, right_mem_uIcc, image_sub_const_uIcc, monotoneOn_or_antitoneOn_iff_uIcc, uIcc_subset_uIcc_iff_le', uIoc_subset_uIcc, ContinuousOn.surjOn_uIcc, PNat.card_fintype_uIcc, image_mul_const_uIcc, uIcc_subset_uIcc_union_uIcc, uIcc_self, Rat.preimage_cast_uIcc, bdd_below_bdd_above_iff_subset_uIcc, AbsolutelyContinuousOnInterval.uniformContinuousOn, left_mem_uIcc, uIcc_ofDual, Monotone.image_uIcc_subset, uIcc_subset_Icc, NNRat.preimage_cast_uIcc, image_const_add_uIcc, Path.range_subpath, AffineMap.image_uIcc, uIcc_toDual, monotone_or_antitone_iff_uIcc, continuousOn_uIcc_extendFrom_uIoo, OrderEmbedding.preimage_uIcc, Fin.preimage_natAdd_uIcc_natAdd, uIcc_eq_union, uIcc_subset_uIcc_iff_le, image_mulSingle_uIcc_right, isPreconnected_uIcc, convex_uIcc, uIoo_subset_uIcc, measurableSet_uIcc, uIoo_subset_uIcc_self, preimage_const_mul_uIcc, Real.volume_real_interval, image_const_sub_uIcc, pi_univ_uIcc, inv_uIcc, Filter.tendsto_Ioc_uIcc_uIcc, preimage_const_sub_uIcc, Fin.image_addNat_uIcc, image_add_const_uIcc, Filter.tendsto_Icc_uIcc_uIcc, image_single_uIcc_left, image_update_uIcc_left, Fin.image_succ_uIcc, Continuous.integrableOn_uIcc, Fin.image_val_uIcc, Fintype.card_uIcc, AbsolutelyContinuousOnInterval.uniformlyContinuousOn, image_single_uIcc, Icc_subset_uIcc', nonempty_uIcc, ordConnected_iff_uIcc_subset_right, Monotone.mapsTo_uIcc, Fin.image_natAdd_uIcc, segment_subset_uIcc, quasilinearOn_iff_mem_uIcc, image_update_uIcc, image_update_uIcc_right, preimage_sub_const_uIcc, uIcc_prod_eq, preimage_div_const_uIcc, finite_interval, Fin.preimage_castAdd_uIcc_castAdd, Fin.preimage_cast_uIcc, ordConnected_iff_uIcc_subset, ordConnectedProj_eq, Fin.preimage_rev_uIcc, uIcc_of_gt, MeasureTheory.uIoc_ae_eq_interval, Filter.tendsto_uIcc_of_Icc, Fin.image_castLE_uIcc, AbsolutelyContinuousOnInterval.continuousOn, preimage_const_add_uIcc, ENNReal.image_coe_uIcc, mem_uIcc_of_ge, intervalIntegrable_inv_iff, mem_ordConnectedComponent, uIcc_of_not_le, Complex.horizontalSegment_eq, Finset.coe_uIcc, image_subtype_val_uIcc, Real.volume_interval, parallelepiped_single, mem_uIcc, Fin.preimage_castLE_uIcc_castLE, ordConnected_uIcc, Fin.image_castAdd_uIcc
uIoc πŸ“–CompOp
78 mathmath: OrdConnected.uIoc_subset, intervalIntegrable_iff, intervalIntegral.intervalIntegral_eq_integral_uIoc, Fin.image_addNat_uIoc, nonempty_uIoc, interval_average_eq_div, exists_eq_interval_average_of_noAtoms, Fin.image_castLE_uIoc, OrderEmbedding.preimage_uIoc, Ioc_subset_uIoc', Fin.preimage_castSucc_uIoc_castSucc, NNReal.image_coe_uIoc, Fin.preimage_castLE_uIoc_castLE, ENNReal.image_coe_uIoc, Fin.preimage_natAdd_uIoc_natAdd, curveIntegralFun_trans_aeeq_right, AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero, intervalIntegral.abs_intervalIntegral_eq, uIoc_union_uIoc, uIoc_comm, Fin.preimage_addNat_uIoc_addNat, closure_uIoc, intervalIntegral.integral_cases, right_mem_uIoc, Ioc_subset_uIoc, interval_average_symm, uIoc_subset_uIcc, uIoc_injective_right, measurableSet_uIoc, left_mem_uIoc, intervalIntegral.norm_intervalIntegral_eq, image_subtype_val_uIoc, AbsolutelyContinuousOnInterval.tendsto_volume_restrict_totalLengthFilter_disjWithin_nhds_zero, aemeasurable_uIoc_iff, AbsolutelyContinuousOnInterval.biUnion_uIoc_subset_of_mem_disjWithin, intervalIntegrable_const_iff, Continuous.integrableOn_uIoc, Rat.preimage_cast_uIoc, Fin.image_castAdd_uIoc, uIoc_subset_uIoc_of_uIcc_subset_uIcc, MeasureTheory.ae_restrict_uIoc_iff, uIoc_injective_left, Fin.preimage_cast_uIoc, Fin.preimage_succ_uIoc_succ, Fin.preimage_val_uIoc_val, injOn_circleMap_of_abs_sub_le, mem_uIoc, exists_eq_interval_average_of_measure, isPreconnected_uIoc, Real.circleAverage_eq_intervalAverage, IntervalIntegrable.def', intervalIntegral.abs_integral_eq_abs_integral_uIoc, AbsolutelyContinuousOnInterval.uIoc_subset_of_mem_disjWithin, curveIntegralFun_trans_aeeq_left, intervalIntegral.norm_integral_eq_norm_integral_uIoc, Fin.image_val_uIoc, IntervalIntegrable.aestronglyMeasurable_restrict_uIoc, Fin.preimage_castAdd_uIoc_castAdd, Real.volume_uIoc, unitInterval.volume_uIoc, interval_average_eq, strictConvex_uIoc, exists_eq_interval_average, isConnected_uIoc, MeasureTheory.uIoc_ae_eq_interval, Fin.image_succ_uIoc, MeasureTheory.ae_restrict_uIoc_eq, intervalIntegral.norm_integral_le_integral_norm_uIoc, uIoc_of_le, integral_pow_abs_sub_uIoc, Fin.image_natAdd_uIoc, uIoc_of_ge, uIoc_eq_union, ordConnected_uIoc, NNRat.preimage_cast_uIoc, notMem_uIoc, Fin.image_castSucc_uIoc, MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_uIoc_iff
uIoo πŸ“–CompOp
53 mathmath: right_notMem_uIoo, Fin.preimage_castSucc_uIoo_castSucc, isPreconnected_uIoo, nhdsWithin_uIoo_right_le_nhdsNE, uIoo_subset_Ioo, Fin.preimage_natAdd_uIoo_natAdd, exists_eq_interval_average_of_noAtoms, mem_uIoo_of_gt, Fin.image_succ_uIoo, uIoo_of_ge, uIoo_eq_union, closure_uIoo, uIoo_of_not_ge, nonempty_uIoo, Ioo_min_max, Fin.image_val_uIoo, unitInterval.volume_uIoo, uIoo_of_lt, Fin.preimage_cast_uIoo, uIoo_toDual, image_subtype_val_uIoo, Fin.preimage_castAdd_uIoo_castAdd, Ioo_subset_uIoo, ENNReal.image_coe_uIoo, Fin.preimage_val_uIoo_val, mem_uIoo_of_lt, exists_isLocalExtr_uIoo, Fin.image_castLE_uIoo, uIoo_subset_uIcc, Fin.image_castAdd_uIoo, uIoo_subset_uIcc_self, uIoo_of_not_le, uIoo_comm, Fin.image_castSucc_uIoo, Fin.image_natAdd_uIoo, nhdsWithin_uIoo_left_le_nhdsNE, Real.volume_uIoo, exists_rat_mem_uIoo, Fin.image_addNat_uIoo, left_notMem_uIoo, uIoo_ofDual, Fin.preimage_addNat_uIoo_addNat, uIoo_of_gt, Fin.preimage_rev_uIoo, uIoo_self, uIoo_of_le, exists_eq_interval_average, isConnected_uIoo, Fin.preimage_castLE_uIoo_castLE, exists_uIoo_isExtrOn_uIcc, NNReal.image_coe_uIoo, Ioo_subset_uIoo', Fin.preimage_succ_uIoo_succ

Theorems

NameKindAssumesProvesValidatesDepends On
Icc_min_max πŸ“–mathematicalβ€”Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
uIcc
β€”β€”
Icc_subset_uIcc πŸ“–mathematicalβ€”Set
instHasSubset
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
β€”Icc_subset_Icc
inf_le_left
le_sup_right
Icc_subset_uIcc' πŸ“–mathematicalβ€”Set
instHasSubset
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
β€”Icc_subset_Icc
inf_le_right
le_sup_left
Ioc_subset_uIoc πŸ“–mathematicalβ€”Set
instHasSubset
Ioc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoc
β€”Ioc_subset_Ioc
min_le_left
le_max_right
Ioc_subset_uIoc' πŸ“–mathematicalβ€”Set
instHasSubset
Ioc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoc
β€”Ioc_subset_Ioc
min_le_right
le_max_left
Ioo_min_max πŸ“–mathematicalβ€”Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
uIoo
β€”β€”
Ioo_subset_uIoo πŸ“–mathematicalβ€”Set
instHasSubset
Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoo
β€”Ioo_subset_Ioo
inf_le_left
le_sup_right
Ioo_subset_uIoo' πŸ“–mathematicalβ€”Set
instHasSubset
Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoo
β€”Ioo_subset_Ioo
inf_le_right
le_sup_left
bdd_below_bdd_above_iff_subset_uIcc πŸ“–mathematicalβ€”BddBelow
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BddAbove
Set
instHasSubset
uIcc
β€”bddBelow_bddAbove_iff_subset_Icc
Icc_subset_uIcc
eq_of_mem_uIcc_of_mem_uIcc πŸ“–β€”Set
instMembership
uIcc
DistribLattice.toLattice
β€”β€”eq_of_inf_eq_sup_eq
inf_congr_right
sup_congr_right
eq_of_mem_uIcc_of_mem_uIcc' πŸ“–β€”Set
instMembership
uIcc
DistribLattice.toLattice
β€”β€”uIcc_comm
eq_of_mem_uIcc_of_mem_uIcc
eq_of_mem_uIoc_of_mem_uIoc πŸ“–β€”Set
instMembership
uIoc
β€”β€”le_antisymm
le_of_lt
le_trans
eq_of_mem_uIoc_of_mem_uIoc' πŸ“–β€”Set
instMembership
uIoc
β€”β€”uIoc_comm
eq_of_mem_uIoc_of_mem_uIoc
eq_of_notMem_uIoc_of_notMem_uIoc πŸ“–β€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
instMembership
uIoc
β€”β€”β€”
forall_uIoc_iff πŸ“–β€”β€”β€”β€”uIoc_eq_union
left_mem_uIcc πŸ“–mathematicalβ€”Set
instMembership
uIcc
β€”inf_le_left
le_sup_left
left_mem_uIoc πŸ“–mathematicalβ€”Set
instMembership
uIoc
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”
left_notMem_uIoo πŸ“–mathematicalβ€”Set
instMembership
uIoo
β€”β€”
mem_uIcc πŸ“–mathematicalβ€”Set
instMembership
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
β€”uIcc_eq_union
mem_uIcc_of_ge πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Set
instMembership
uIcc
β€”Icc_subset_uIcc'
mem_uIcc_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Set
instMembership
uIcc
β€”Icc_subset_uIcc
mem_uIoc πŸ“–mathematicalβ€”Set
instMembership
uIoc
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
β€”uIoc_eq_union
mem_union
mem_Ioc
mem_uIoo_of_gt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
instMembership
uIoo
β€”Ioo_subset_uIoo'
mem_uIoo_of_lt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
instMembership
uIoo
β€”Ioo_subset_uIoo
monotoneOn_or_antitoneOn_iff_uIcc πŸ“–mathematicalβ€”MonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AntitoneOn
Set
instMembership
uIcc
β€”β€”
monotone_or_antitone_iff_uIcc πŸ“–mathematicalβ€”Monotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Antitone
Set
instMembership
uIcc
β€”Monotone.map_min
Monotone.map_max
Antitone.map_min
Antitone.map_max
Mathlib.Tactic.Contrapose.contrapose₁
Mathlib.Tactic.Push.not_forall_eq
not_monotone_not_antitone_iff_exists_le_le
Icc_subset_uIcc
LE.le.not_gt
max_lt
lt_min
nonempty_uIcc πŸ“–mathematicalβ€”Nonempty
uIcc
β€”nonempty_Icc
inf_le_sup
nonempty_uIoc πŸ“–mathematicalβ€”Nonempty
uIoc
β€”β€”
nonempty_uIoo πŸ“–mathematicalβ€”Nonempty
uIoo
β€”β€”
notMem_uIcc_of_gt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
instMembership
uIcc
β€”notMem_Icc_of_gt
max_lt_iff
notMem_uIcc_of_lt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
instMembership
uIcc
β€”notMem_Icc_of_lt
lt_min_iff
notMem_uIoc πŸ“–mathematicalβ€”Set
instMembership
uIoc
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
β€”uIoc_eq_union
right_mem_uIcc πŸ“–mathematicalβ€”Set
instMembership
uIcc
β€”inf_le_right
le_sup_right
right_mem_uIoc πŸ“–mathematicalβ€”Set
instMembership
uIoc
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”
right_notMem_uIoo πŸ“–mathematicalβ€”Set
instMembership
uIoo
β€”β€”
uIcc_comm πŸ“–mathematicalβ€”uIccβ€”inf_comm
sup_comm
uIcc_eq_union πŸ“–mathematicalβ€”uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
instUnion
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
β€”Icc_union_Icc'
le_refl
max_comm
uIcc_injective_left πŸ“–mathematicalβ€”Set
uIcc
DistribLattice.toLattice
β€”uIcc_comm
uIcc_injective_right
uIcc_injective_right πŸ“–mathematicalβ€”Set
uIcc
DistribLattice.toLattice
β€”eq_of_mem_uIcc_of_mem_uIcc
ext_iff
left_mem_uIcc
uIcc_ofDual πŸ“–mathematicalβ€”uIcc
DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
preimage
OrderDual.toDual
OrderDual.instLattice
β€”Icc_ofDual
uIcc_of_ge πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
Icc
β€”uIcc.eq_1
inf_eq_right
sup_eq_left
uIcc_of_gt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
Icc
β€”uIcc_of_ge
LT.lt.le
uIcc_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
Icc
β€”uIcc.eq_1
inf_eq_left
sup_eq_right
uIcc_of_lt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
uIcc
Icc
β€”uIcc_of_le
LT.lt.le
uIcc_of_not_ge πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIcc
Icc
β€”uIcc_of_lt
lt_of_not_ge
uIcc_of_not_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIcc
Icc
β€”uIcc_of_gt
lt_of_not_ge
uIcc_prod_eq πŸ“–mathematicalβ€”uIcc
Prod.instLattice
SProd.sprod
Set
instSProd
β€”uIcc_prod_uIcc
uIcc_prod_uIcc πŸ“–mathematicalβ€”SProd.sprod
Set
instSProd
uIcc
Prod.instLattice
β€”Icc_prod_Icc
uIcc_self πŸ“–mathematicalβ€”uIcc
Set
instSingletonSet
β€”inf_of_le_left
sup_of_le_left
Icc_self
uIcc_subset_Icc πŸ“–mathematicalSet
instMembership
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
instHasSubset
uIcc
β€”Icc_subset_Icc
le_inf
sup_le
uIcc_subset_uIcc πŸ“–mathematicalSet
instMembership
uIcc
instHasSubsetβ€”Icc_subset_Icc
le_inf
sup_le
uIcc_subset_uIcc_iff_le πŸ“–mathematicalβ€”Set
instHasSubset
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”uIcc_subset_uIcc_iff_le'
uIcc_subset_uIcc_iff_le' πŸ“–mathematicalβ€”Set
instHasSubset
uIcc
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Icc_subset_Icc_iff
inf_le_sup
uIcc_subset_uIcc_iff_mem πŸ“–mathematicalβ€”Set
instHasSubset
uIcc
instMembership
β€”left_mem_uIcc
right_mem_uIcc
uIcc_subset_uIcc
uIcc_subset_uIcc_left πŸ“–mathematicalSet
instMembership
uIcc
instHasSubsetβ€”uIcc_subset_uIcc
left_mem_uIcc
uIcc_subset_uIcc_right πŸ“–mathematicalSet
instMembership
uIcc
instHasSubsetβ€”uIcc_subset_uIcc
right_mem_uIcc
uIcc_subset_uIcc_union_uIcc πŸ“–mathematicalβ€”Set
instHasSubset
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instUnion
β€”le_total
uIcc_toDual πŸ“–mathematicalβ€”uIcc
OrderDual
OrderDual.instLattice
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
preimage
OrderDual.ofDual
β€”Icc_toDual
uIoc_comm πŸ“–mathematicalβ€”uIocβ€”min_comm
max_comm
uIoc_eq_union πŸ“–mathematicalβ€”uIoc
Set
instUnion
Ioc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”le_total
inf_of_le_left
sup_of_le_right
Ioc_eq_empty
union_empty
inf_of_le_right
sup_of_le_left
empty_union
uIoc_injective_left πŸ“–mathematicalβ€”Set
uIoc
β€”uIoc_comm
uIoc_injective_right
uIoc_injective_right πŸ“–mathematicalβ€”Set
uIoc
β€”le_or_gt
Iff.not
ext_iff
LE.le.eq_of_not_lt
uIoc_of_le
not_le
eq_of_mem_uIoc_of_mem_uIoc
left_mem_uIoc
LT.lt.trans_le
LT.lt.not_ge
uIoc_of_ge πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoc
Ioc
β€”inf_of_le_right
sup_of_le_left
uIoc_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoc
Ioc
β€”inf_of_le_left
sup_of_le_right
uIoc_subset_uIcc πŸ“–mathematicalβ€”Set
instHasSubset
uIoc
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Ioc_subset_Icc_self
uIoc_subset_uIoc_of_uIcc_subset_uIcc πŸ“–mathematicalSet
instHasSubset
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIocβ€”Ioc_subset_Ioc
uIcc_subset_uIcc_iff_le
uIoc_union_uIoc πŸ“–mathematicalSet
instMembership
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instUnion
uIoc
β€”uIoc_of_le
uIcc_of_le
Ioc_union_Ioc_eq_Ioc
uIoc_comm
union_comm
uIcc_comm
le_of_not_ge
uIoo_comm πŸ“–mathematicalβ€”uIooβ€”inf_comm
sup_comm
uIoo_eq_union πŸ“–mathematicalβ€”uIoo
Set
instUnion
Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”lt_or_ge
uIoo_of_lt
Ioo_eq_empty_of_le
LT.lt.le
union_empty
uIoo_of_ge
Ioo_eq_empty
empty_union
uIoo_ofDual πŸ“–mathematicalβ€”uIoo
DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
preimage
OrderDual.toDual
OrderDual.instLinearOrder
β€”Ioo_ofDual
uIoo_of_ge πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoo
Ioo
β€”uIoo.eq_1
inf_eq_right
sup_eq_left
uIoo_of_gt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoo
Ioo
β€”uIoo_of_ge
LT.lt.le
uIoo_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoo
Ioo
β€”uIoo.eq_1
inf_eq_left
sup_eq_right
uIoo_of_lt πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoo
Ioo
β€”uIoo_of_le
LT.lt.le
uIoo_of_not_ge πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoo
Ioo
β€”uIoo_of_lt
lt_of_not_ge
uIoo_of_not_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
uIoo
Ioo
β€”uIoo_of_gt
lt_of_not_ge
uIoo_self πŸ“–mathematicalβ€”uIoo
Set
instEmptyCollection
β€”min_self
max_self
Ioo_eq_empty
uIoo_subset_Ioo πŸ“–mathematicalSet
instMembership
Icc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instHasSubset
uIoo
Ioo
β€”Ioo_subset_Ioo
le_inf
sup_le
uIoo_subset_uIcc πŸ“–mathematicalβ€”Set
instHasSubset
uIoo
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”uIoo_subset_uIcc_self
uIoo_subset_uIcc_self πŸ“–mathematicalβ€”Set
instHasSubset
uIoo
uIcc
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”β€”
uIoo_toDual πŸ“–mathematicalβ€”uIoo
OrderDual
OrderDual.instLinearOrder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
preimage
OrderDual.ofDual
β€”Ioo_toDual

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