Documentation Verification Report

Disjoint

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

Statistics

MetricCount
DefinitionsDisjoint, Disjoint, Disjoint, Disjoint, Disjoint
5
TheoremsbiUnion_Ici_eq_Ici, biUnion_Ici_eq_Ioi, biUnion_Ioi_eq, iUnion_Ioi_eq, biUnion_Iic_eq_Iic, biUnion_Iic_eq_Iio, biUnion_Iio_eq, iUnion_Iio_eq, Ici_disjoint_Iic, Ico_disjoint_Ico, Ico_disjoint_Ico_same, Iic_disjoint_Ici, Iic_disjoint_Ioc, Iic_disjoint_Ioi, Iio_disjoint_Ici, Iio_disjoint_Ioi_iff, Iio_disjoint_Ioi_of_le, Iio_disjoint_Ioi_of_not_lt, Iio_disjoint_Ioi_same, Ioc_disjoint_Ioc, Ioc_disjoint_Ioc_of_le, Ioc_disjoint_Ioi, Ioc_disjoint_Ioi_same, Ioi_disjoint_Iio_iff, Ioi_disjoint_Iio_of_le, Ioi_disjoint_Iio_of_not_lt, Ioi_disjoint_Iio_same, Ioo_disjoint_Ioo, biUnion_Ico_eq_Iio_self_iff, biUnion_Ioc_eq_Ioi_self_iff, eq_of_Ico_disjoint, iUnion_Icc_left, iUnion_Icc_right, iUnion_Ici, iUnion_Ico_eq_Iio_self_iff, iUnion_Ico_left, iUnion_Ico_right, iUnion_Iic, iUnion_Iio, iUnion_Ioc_eq_Ioi_self_iff, iUnion_Ioc_left, iUnion_Ioc_right, iUnion_Ioi, iUnion_Ioo_left, iUnion_Ioo_right, iInter_Iic_eq_empty_iff, iInter_Iio_of_not_bddBelow_range, iUnion_Ici_eq_Ici_iInf, iUnion_Ici_eq_Ioi_iInf, iUnion_Iic_eq_Iic_iSup, iUnion_Iic_eq_Iio_iSup, iUnion_Iic_of_not_bddAbove_range, iUnion_Iio_eq_univ_iff
53
Total58

AList

Definitions

NameCategoryTheorems
Disjoint πŸ“–MathDefβ€”

CantorScheme

Definitions

NameCategoryTheorems
Disjoint πŸ“–MathDefβ€”

Equiv.Perm

Definitions

NameCategoryTheorems
Disjoint πŸ“–MathDef
20 mathmath: disjoint_refl_iff, disjoint_ofSubtype_noncommPiCoprod, disjoint_inv_right_iff, disjoint_one_left, disjoint_ofSubtype_of_memFixedPoints_self, cycleFactorsFinset_eq_finset, disjoint_swap_swap, instSymmDisjoint, mem_cycleType_iff, disjoint_comm, disjoint_conj, cycleFactorsFinset_pairwise_disjoint, Disjoint.symmetric, disjoint_inv_left_iff, disjoint_one_right, cycleFactorsFinset_eq_list_toFinset, disjoint_mul_inv_of_mem_cycleFactorsFinset, disjoint_iff_disjoint_support, List.formPerm_disjoint_iff, disjoint_iff_eq_or_eq

Finmap

Definitions

NameCategoryTheorems
Disjoint πŸ“–MathDef
4 mathmath: Disjoint.symm_iff, disjoint_union_right, disjoint_empty, disjoint_union_left

IsGLB

Theorems

NameKindAssumesProvesValidatesDepends On
biUnion_Ici_eq_Ici πŸ“–mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.iUnion
Set.Ici
β€”HasSubset.Subset.antisymm
Set.instAntisymmSubset
Set.iUnionβ‚‚_subset
Set.Ici_subset_Ici
mem_lowerBounds
Set.mem_iUnionβ‚‚
biUnion_Ici_eq_Ioi πŸ“–mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.iUnion
Set.Ici
Set.Ioi
β€”HasSubset.Subset.antisymm
Set.instAntisymmSubset
Set.iUnionβ‚‚_subset
Set.Ici_subset_Ioi
lt_of_le_of_ne
exists_between
Set.mem_iUnionβ‚‚
LT.lt.le
biUnion_Ioi_eq πŸ“–mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.iUnion
Set
Set.instMembership
Set.Ioi
β€”HasSubset.Subset.antisymm
Set.instAntisymmSubset
Set.iUnionβ‚‚_subset
Set.Ioi_subset_Ioi
exists_between
Set.mem_biUnion
iUnion_Ioi_eq πŸ“–mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.range
Set.iUnion
Set.Ioi
β€”Set.biUnion_range
biUnion_Ioi_eq

IsLUB

Theorems

NameKindAssumesProvesValidatesDepends On
biUnion_Iic_eq_Iic πŸ“–mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.iUnion
Set.Iic
β€”IsGLB.biUnion_Ici_eq_Ici
dual
biUnion_Iic_eq_Iio πŸ“–mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instMembership
Set.iUnion
Set.Iic
Set.Iio
β€”IsGLB.biUnion_Ici_eq_Ioi
dual
biUnion_Iio_eq πŸ“–mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.iUnion
Set
Set.instMembership
Set.Iio
β€”IsGLB.biUnion_Ioi_eq
dual
iUnion_Iio_eq πŸ“–mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.range
Set.iUnion
Set.Iio
β€”IsGLB.iUnion_Ioi_eq
dual

Set

Theorems

NameKindAssumesProvesValidatesDepends On
Ici_disjoint_Iic πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ici
Iic
Preorder.toLE
β€”disjoint_iff_inter_eq_empty
Ici_inter_Iic
Icc_eq_empty_iff
Ico_disjoint_Ico πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ico
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Ico_inter_Ico
Ico_disjoint_Ico_same πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ico
β€”disjoint_left
LT.lt.not_ge
Iic_disjoint_Ici πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Iic
Ici
Preorder.toLE
β€”disjoint_comm
Ici_disjoint_Iic
Iic_disjoint_Ioc πŸ“–mathematicalPreorder.toLEDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Iic
Ioc
β€”Disjoint.mono
le_rfl
Ioc_subset_Ioi_self
Iic_disjoint_Ioi
Iic_disjoint_Ioi πŸ“–mathematicalPreorder.toLEDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Iic
Ioi
β€”disjoint_left
LT.lt.not_ge
LE.le.trans_lt
Iio_disjoint_Ici πŸ“–mathematicalPreorder.toLEDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Iio
Ici
β€”disjoint_left
LT.lt.not_ge
LE.le.trans_lt'
Iio_disjoint_Ioi_iff πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Iio
Ioi
Preorder.toLT
β€”disjoint_comm
Ioi_disjoint_Iio_iff
Iio_disjoint_Ioi_of_le πŸ“–mathematicalPreorder.toLEDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Iio
Ioi
β€”disjoint_comm
Ioi_disjoint_Iio_of_le
Iio_disjoint_Ioi_of_not_lt πŸ“–mathematicalPreorder.toLTDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Iio
Ioi
β€”disjoint_comm
Ioi_disjoint_Iio_of_not_lt
Iio_disjoint_Ioi_same πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Iio
Ioi
β€”Iio_disjoint_Ioi_of_le
le_rfl
Ioc_disjoint_Ioc πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Ico_disjoint_Ico
Ico_toDual
Ioc_disjoint_Ioc_of_le πŸ“–mathematicalPreorder.toLEDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioc
β€”Disjoint.mono
Ioc_subset_Iic_self
le_rfl
Iic_disjoint_Ioc
Ioc_disjoint_Ioi πŸ“–mathematicalPreorder.toLEDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioc
Ioi
β€”disjoint_left
LE.le.not_gt
LE.le.trans
Ioc_disjoint_Ioi_same πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioc
Ioi
β€”Ioc_disjoint_Ioi
le_rfl
Ioi_disjoint_Iio_iff πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioi
Iio
Preorder.toLT
β€”exists_between
Disjoint.notMem_of_mem_left
Ioi_disjoint_Iio_of_not_lt
Ioi_disjoint_Iio_of_le πŸ“–mathematicalPreorder.toLEDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioi
Iio
β€”Ioi_disjoint_Iio_of_not_lt
not_lt_of_ge
Ioi_disjoint_Iio_of_not_lt πŸ“–mathematicalPreorder.toLTDisjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioi
Iio
β€”disjoint_left
LT.lt.trans
Ioi_disjoint_Iio_same πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioi
Iio
β€”Ioi_disjoint_Iio_of_le
le_rfl
Ioo_disjoint_Ioo πŸ“–mathematicalβ€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ioo
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
β€”Ioo_inter_Ioo
biUnion_Ico_eq_Iio_self_iff πŸ“–mathematicalβ€”iUnion
Ico
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Iio
Preorder.toLE
β€”iUnion_congr_Prop
biUnion_Ioc_eq_Ioi_self_iff πŸ“–mathematicalβ€”iUnion
Ioc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Ioi
Preorder.toLE
β€”iUnion_congr_Prop
eq_of_Ico_disjoint πŸ“–β€”Disjoint
Set
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Ico
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
instMembership
β€”β€”le_antisymm
le_max_iff
min_eq_left
le_of_lt
Ico_disjoint_Ico
not_lt_of_ge
iUnion_Icc_left πŸ“–mathematicalβ€”iUnion
Icc
Iic
β€”iUnion_Ici
univ_inter
iUnion_Icc_right πŸ“–mathematicalβ€”iUnion
Icc
Ici
β€”iUnion_Iic
inter_univ
iUnion_Ici πŸ“–mathematicalβ€”iUnion
Ici
univ
β€”iUnion_eq_univ_iff
self_mem_Ici
iUnion_Ico_eq_Iio_self_iff πŸ“–mathematicalβ€”iUnion
Ico
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Iio
Preorder.toLE
β€”β€”
iUnion_Ico_left πŸ“–mathematicalβ€”iUnion
Ico
Iio
β€”iUnion_Ici
univ_inter
iUnion_Ico_right πŸ“–mathematicalβ€”iUnion
Ico
Ici
β€”iUnion_Iio
inter_univ
iUnion_Iic πŸ“–mathematicalβ€”iUnion
Iic
univ
β€”iUnion_eq_univ_iff
self_mem_Iic
iUnion_Iio πŸ“–mathematicalβ€”iUnion
Iio
univ
β€”iUnion_eq_univ_iff
NoMaxOrder.exists_gt
iUnion_Ioc_eq_Ioi_self_iff πŸ“–mathematicalβ€”iUnion
Ioc
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Ioi
Preorder.toLE
β€”β€”
iUnion_Ioc_left πŸ“–mathematicalβ€”iUnion
Ioc
Iic
β€”iUnion_Ioi
univ_inter
iUnion_Ioc_right πŸ“–mathematicalβ€”iUnion
Ioc
Ioi
β€”iUnion_Iic
inter_univ
iUnion_Ioi πŸ“–mathematicalβ€”iUnion
Ioi
univ
β€”iUnion_eq_univ_iff
NoMinOrder.exists_lt
iUnion_Ioo_left πŸ“–mathematicalβ€”iUnion
Ioo
Iio
β€”iUnion_Ioi
univ_inter
iUnion_Ioo_right πŸ“–mathematicalβ€”iUnion
Ioo
Ioi
β€”iUnion_Iio
inter_univ

(root)

Definitions

NameCategoryTheorems
Disjoint πŸ“–MathDef
800 mathmath: IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Set.pairwiseDisjoint_range_iff, Matroid.exists_isBasis_disjoint_isBasis_of_subset, Metric.ball_disjoint_ball, Set.pairwise_disjoint_Ioc_zpow, Submodule.disjoint_span_singleton', Set.pairwise_disjoint_Ioo_add_zsmul, Metric.disjoint_ball_infDist, Module.End.isSemisimple_restrict_iff, Set.disjoint_ordT5Nhd, Finset.zero_mem_sub_iff, Finset.disjoint_insert_erase, Finset.disjoint_map, MonoidHom.ker_transferSylow_disjoint, LocalizedModule.subsingleton_iff_disjoint, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, Sym2.disjoint_diagSet_fromRel, Multiset.disjoint_finset_sum_left, Set.disjoint_compl_left_iff_subset, SimpleGraph.isBipartiteWith_neighborSet_disjoint, SeparatedNhds.disjoint, PrimeSpectrum.localization_specComap_range, Set.pairwise_disjoint_Ico_zsmul, Set.disjoint_or_nonempty_inter, disjoint_sdiff_self_right, Polynomial.disjoint_ker_aeval_of_isCoprime, disjoint_or_subset_of_isClopen, BoxIntegral.Box.disjoint_splitCenterBox, Matroid.isBase_compl_iff_maximal_disjoint_isBase, LinearMap.injective_restrict_iff_disjoint, SeminormedGroup.disjoint_nhds, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, disjoint_sdiff_iff_le, Set.pairwise_disjoint_Ioo_mul_zpow, LieAlgebra.InvariantForm.orthogonal_disjoint, MeasureTheory.Measure.mutuallySingular_tfae, Finset.supIndep_univ_fin_two, iSupIndep.disjoint_biSup, Filter.disjoint_comap_iff, UniqueFactorizationMonoid.disjoint_normalizedFactors, UpperSet.sdiff_eq_left, MeasureTheory.pairwise_disjoint_fundamentalInterior, Submodule.orthogonal_disjoint, Finset.disjoint_erase_insert, SeparatedNhds.disjoint_closure_left, Module.End.invtSubmodule.disjoint_mk_iff, DFinsupp.disjoint_iff, Set.Iio_disjoint_Ioi_of_not_lt, Directed.disjoint_iSup_right, Finset.disjoint_coe, SimpleGraph.isBipartiteWith_neighborFinset_disjoint, Set.disjoint_union_right, Set.disjoint_of_subset_iff_left_eq_empty, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, IsUltrametricDist.ball_subset_trichotomy, Finset.disjoint_union_right, Matroid.IsBasis.contract_dep_iff, AddCommMonoid.primaryComponent.disjoint, BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff, IsModularLattice.exists_disjoint_and_sup_eq, Finset.symmDiff_eq_union_iff, SimpleGraph.ComponentCompl.disjoint_right, LieModule.disjoint_genWeightSpaceOf, LowerSet.disjoint_coe, Filter.disjoint_cocompact_left, Codisjoint.dual, disjoint_nhds_cocompact, IsAtom.not_le_iff_disjoint, EMetric.ball_disjoint, Finset.disjoint_filter_filter_neg, Matroid.contract_isCocircuit_iff, BoxIntegral.Box.disjoint_withBotCoe, Antitone.pairwise_disjoint_on_Ioc_pred, disjoint_left_comm, Topology.RelCWComplex.disjoint_openCell_of_ne, IsCompact.separation_of_notMem, Set.disjoint_singleton_right, AddAction.IsBlock.disjoint_vadd_left, t1Space_iff_disjoint_nhds_pure, Finset.disjSups_singleton, sSup_disjoint_iff, Set.Iio_disjoint_Ioi_iff, exists_partition_approximatesLinearOn_of_hasFDerivWithinAt, Filter.disjoint_principal_left, isSeparatedMap_iff_disjoint_nhds, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, MeasureTheory.exists_null_pairwise_disjoint_diff, iSupIndep.pairwiseDisjoint, Finset.one_mem_div_iff, IsAtom.disjoint_of_ne, pairwise_disjoint_fiber, Matroid.IsBasis.contract_indep_iff, Finset.exists_disjoint_union_of_even_card, LieSubmodule.disjoint_toSubmodule, separated_by_continuous, Antitone.pairwise_disjoint_on_Ioo_pred, Perfect.small_diam_splitting, Filter.disjoint_comap_iff_map', SimpleGraph.ComponentCompl.pairwise_disjoint, Finset.disjoint_image, Set.Iic_disjoint_Ioi, T25Space.t2_5, disjoint_compl_right_iff, Finset.disjoint_self_iff_empty, Set.disjoint_pi_univ_Ioc_update_left_right, SetRel.prod_comp_prod, Multiset.disjoint_add_left, disjoint_nested_nhds_of_not_inseparable, RootPairing.disjoint_corootSpan_ker_corootForm, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, Set.disjoint_image_left, Multiset.range_disjoint_map_add, Multiset.disjoint_singleton, exists_disjoint_vadd_of_isCompact, DirectedOn.disjoint_sSup_left, MulAction.IsBlock.disjoint_smul_of_ne, Metric.disjoint_cobounded_nhdsSet, Set.Icc.disjoint_iff, Heyting.IsRegular.disjoint_compl_right_iff, Function.update_updateFinset, disjoint_bot_right, disjoint_symmDiff_inf, Matroid.IsMinor.exists_eq_contract_delete_disjoint, le_iff_disjoint_sdiff, isEmbedding_sumElim, Matroid.delete_eq_self_iff, disjoint_rootsOfUnity_of_coprime, MulAction.isBlock_iff_smul_eq_or_disjoint, disjoint_interior_frontier, Finsupp.disjoint_iff, Matroid.contract_eq_self_iff, RootedTree.mem_subtrees_disjoint_iff, AlgebraicIndependent.adjoin_iff_disjoint, Set.pairwise_disjoint_Ioc_zsmul, Set.subset_compl_iff_disjoint_right, Filter.HasBasis.disjoint_iff_right, Set.Ioc_disjoint_Ioc, disjoint_top, Finset.disjiUnion_disjiUnion, Set.disjoint_left, UpperSet.codisjoint_coe, Set.disjoint_singleton_left, Set.disjoint_right, LinearMap.disjoint_inl_inr, Matroid.Coindep.delete_spanning_iff, disjoint_toDual_iff, Monotone.pairwise_disjoint_on_Ioc_pred, Set.disjoint_right_ordSeparatingSet, LowerSet.sdiff_eq_left, Antitone.pairwise_disjoint_on_Ioo_succ, RootPairing.exist_set_root_not_disjoint_and_le_ker_coroot'_of_invtSubmodule, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card, Finset.Ico_disjoint_Ico_consecutive, Set.disjoint_sdiff_inter, Metric.disjoint_nhds_cobounded, disjoint_sup_right, Filter.disjoint_atTop_principal_Iio, Set.pairwise_disjoint_Ioo_add_intCast, Set.pairwise_disjoint_vadd_iff, Multiset.add_eq_union_iff_disjoint, Multiset.disjoint_list_sum_left, LinearMap.BilinForm.isCompl_orthogonal_iff_disjoint, disjoint_sdiff_comm, SimpleGraph.neighborFinset_disjoint_singleton, Set.disjoint_iUnion_left, HasSubset.Subset.disjoint_compl_right, Finset.zero_mem_neg_add_iff, disjoint_compl_compl_left_iff, isOpen_setOf_disjoint_nhds_nhds, LieModule.disjoint_lowerCentralSeries_maxTrivSubmodule_iff, PairReduction.disjoint_smallBall_logSizeBallSeq, Multiset.disjoint_union_left, MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier, Set.disjoint_singleton, linearIndependent_sum, Finset.sdiff_eq_self_iff_disjoint, sdiff_lt_left, NonarchimedeanGroup.exists_openSubgroup_separating, disjoint_partialSups_right, Multiset.finset_sum_eq_sup_iff_disjoint, SimpleGraph.edgeSet_eq_iff, Ideal.disjoint_powers_iff_notMem, Matroid.Indep.contract_dep_iff, disjoint_nhds_nhds_iff_not_specializes, iSupIndep_pair, mem_codiscrete, Set.pairwise_disjoint_Ioc_add_zsmul, SimpleGraph.disjoint_edge, SeparatedNhds.disjoint_nhdsSet, disjoint_nhdsSet_principal, Set.pairwiseDisjoint_insert_of_notMem, Set.disjoint_powerset_insert, Equiv.Perm.Disjoint.disjoint_cycleFactorsFinset, MulAction.disjoint_image_image_iff, t2_separation_nhds, Set.disjoint_toFinset, SimpleGraph.disjoint_edgeFinset, Set.disjoint_smul_set, AddAction.IsBlock.disjoint_vadd_vadd_set, Multiset.nodup_bind, Set.pairwise_disjoint_Ioc_mul_zpow, Submodule.disjoint_span_singleton, Set.pairwise_disjoint_Ico_mul_zpow, Filter.disjoint_iff, Ideal.disjoint_map_primeCompl_iff_comap_le, SeminormedAddGroup.disjoint_nhds_zero, Filter.not_nonneg_sub_iff, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, not_disjoint_segment_convexHull_triple, compl_eq_sSup_disjoint, disjoint_iff, isClosed_and_discrete_iff, r1Space_iff_inseparable_or_disjoint_nhds, Set.disjoint_sUnion_left, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, TopologicalSpace.Clopens.coe_disjoint, AddSubmonoid.disjoint_def', LowerSet.sdiff_lt_left, SimpleGraph.disjoint_edgeSet, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, disjoint_bot_left, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, isInducing_sumElim, Filter.disjoint_atBot_atTop, Finset.disjoint_or_nonempty_inter, LinearMap.disjoint_ker, AddSubgroup.disjoint_def, disjoint_iSup_iff, Set.Ioi_disjoint_Iio_iff, Matroid.dual_indep_iff_exists', Filter.disjoint_cofinite_right, Finset.one_mem_inv_mul_iff, MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier, IsLindelof.disjoint_nhdsSet_left, Filter.disjoint_map, disjoint_comm, Finset.disjoint_sup_left, disjoint_compl_left, Set.pairwise_disjoint_Ico_add_intCast, SimpleGraph.neighborFinset_boxProd, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion, Filter.disjoint_cofinite_left, disjoint_ofDual_iff, Finset.disjoint_filter, MulAction.orbit.eq_or_disjoint, Nat.disjoint_divisors_filter_isPrimePow, Topology.IsInducing.disjoint_of_sumElim_aux, Finset.mem_disjSups, disjoint_compl_compl_right_iff, Set.subset_diff, separated_by_isOpenEmbedding, IsLocalization.isPrime_iff_isPrime_disjoint, isCompl_iff, SubMulAction.disjoint_val_image, Set.not_disjoint_iff_nonempty_inter, TensorAlgebra.ΞΉ_range_disjoint_one, Subgroup.subgroupOf_eq_bot, IsCompact.disjoint_nhdsSet_left, Numbering.disjoint_prefixed_prefixed, AddAction.IsBlock.disjoint_vadd_set_vadd, iSupIndep_def'', Metric.disjoint_closedEBall_of_lt_infEDist, Set.disjoint_insert_left, IsLindelof.disjoint_nhdsSet_right, Finset.not_disjoint_iff_nonempty_inter, ExteriorAlgebra.ΞΉ_range_disjoint_one, exists_nhds_disjoint_closure, Finset.card_union_eq_card_add_card, SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph, isNowhereDense_iff_disjoint, ConvexCone.disjoint_hull_left_of_convex, Filter.not_disjoint_self_iff, disjoint_disjointed_of_lt, EisensteinSeries.pairwise_disjoint_gammaSet, SimpleGraph.isBipartiteWith_neighborFinset_disjoint', Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_card, disjoint_map_orderIso_iff, MulAction.IsBlock.disjoint_smul_right, IsPrimitiveRoot.disjoint, BoxIntegral.unitPartition.disjoint, linearIndepOn_iff_disjoint, Finset.disjoint_iff_ne, Finset.disjoint_disjiUnion_right, MulAction.IsBlock.disjoint_smul_smul_set, AlgebraicGeometry.disjoint_opensRange_sigmaΞΉ, disjoint_right_comm, Set.Iic.disjoint_iff, iSupIndep_def', le_sdiff, Set.disjoint_iUnion_right, LowerSet.disjoint_prod, exists_open_nhds_disjoint_closure, MeasureTheory.Measure.mutuallySingular_iff_disjoint, not_linearIndependent_iffβ‚’β‚›, disjoint_measurableAtom_of_notMem, List.disjoint_toFinset_iff_disjoint, MeasureTheory.disjoint_cylinder_iff, Subgroup.disjoint_def', Submodule.disjoint_ker_of_finrank_le, Multiset.disjoint_finset_sum_right, Equiv.Perm.ofSign_disjoint, separatedNhds_iff_disjoint, codisjoint_ofDual_iff, NFA.disjoint_evalFrom_reverse_iff, Matroid.contract_spanning_iff, Set.disjoint_prod, Finset.disjoint_filter_filter_not, Filter.nonneg_sub_iff, Module.End.disjoint_genEigenspace, disjoint_nhds_atBot_iff, Real.disjoint_residual_ae, LinearMap.BilinForm.nondegenerate_restrict_iff_disjoint_ker, MulAction.IsBlock.disjoint_smul_set_smul, Set.indicator_eq_zero', Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, Set.PairwiseDisjoint.eq_or_disjoint, Set.Ici.disjoint_iff, disjoint_frontier_iff_isOpen, Multiset.disjoint_sum_left, Set.Intersecting.disjoint_map_compl, Finset.disjoint_map_inl_map_inr, Finset.disjoint_Ioi_Iio, IsGenericPoint.disjoint_iff, clusterPt_iff_not_disjoint, Set.disjoint_image_iff, disjoint_assoc, AddAction.IsBlock.disjoint_vadd_right, iSup_disjoint_iff, Module.End.isFinitelySemisimple_iff, Set.disjoint_pi, Antitone.pairwise_disjoint_on_Ioc_succ, Set.indicator_eq_zero, not_addDissociated_iff_exists_disjoint, Subgroup.disjoint_def, le_symmDiff_iff_right, Module.End.disjoint_iInf_maxGenEigenspace, BoxIntegral.Box.not_disjoint_coe_iff_nonempty_inter, exists_seq_infinite_isOpen_pairwise_disjoint, Set.disjoint_iUnionβ‚‚_right, Finset.disjoint_insert_right, IsUltrametricDist.ball_eq_or_disjoint, Filter.HasBasis.disjoint_iff, AddAction.isBlock_iff_vadd_eq_or_disjoint, Set.exists_union_disjoint_cardinal_eq_of_even, SimpleGraph.pairwise_disjoint_supp_connectedComponent, Finset.disjoint_sdiff, Set.intersecting_iff_pairwise_not_disjoint, Multiset.disjoint_map_map, Set.Ioi_disjoint_Iio_of_le, BoxIntegral.Prepartition.pairwiseDisjoint, Set.disjoint_compl_right_iff_subset, Finset.disjiUnion_singleton, Set.pairwise_disjoint_Ioo_zpow, Metric.ball_disjoint_closedBall, Finset.zero_notMem_sub_iff, Matroid.IsCircuit.disjoint_coloops, Set.disjoint_image_image, UpperSet.lt_sdiff_left, Function.disjoint_mulSupport_iff, SimpleGraph.compl_neighborSet_disjoint, VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype, Set.not_disjoint_iff, CommMonoid.primaryComponent.disjoint, Multiset.Nodup.add_iff, Set.disjoint_iff_inter_eq_empty, t2Space_iff_disjoint_nhds, MulAction.IsBlock.smul_eq_smul_or_disjoint, ConvexCone.disjoint_coe, codisjoint_toDual_iff, MeasureTheory.Measure.mutuallySingular_iff_disjoint_ae, Filter.disjoint_principal_principal, iSupβ‚‚_disjoint_iff, connectedComponent_disjoint, RegularSpace.regular, AddAction.IsBlock.disjoint_vadd_of_ne, IsPGroup.disjoint_of_ne, sSupIndep.disjoint_sSup, Set.zero_mem_neg_add_iff, Set.disjoint_insert_right, Set.pairwise_disjoint_Ioc_intCast, Multiset.pairwise_disjoint_powersetCard, Set.subset_compl_iff_disjoint_left, Prop.disjoint_iff, ProperlyDiscontinuousSMul.exists_nhds_disjoint_image, Topology.RelCWComplex.disjoint_interior_base_closedCell, Filter.disjoint_comap_iff_map, Finset.supIndep_pair, Finset.disjoint_disjiUnion_left, Set.Iic_disjoint_Ioc, Finset.disjoint_range_addLeftEmbedding, SimpleGraph.IsBipartiteWith.disjoint, SeparatedNhds.disjoint_closure_right, Set.Ioc_disjoint_Ioi, LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace, Filter.disjoint_pure_pure, disjoint_compl_left_iff, Set.pairwise_disjoint_Ioo_zsmul, Set.Iic_disjoint_Ici, Pi.support_single_disjoint, Multiset.disjoint_left, Submodule.disjoint_def', HasSubset.Subset.disjoint_compl_left, disjoint_ball_closedBall_iff, SimpleGraph.fromEdgeSet_disjoint, BoxIntegral.Box.disjoint_splitLower_splitUpper, Finset.Iic_disjoint_Ioc, R1Space.specializes_or_disjoint_nhds, SimpleGraph.isBipartiteWith_neighborSet_disjoint', Set.disjoint_univ, Interval.disjoint_coe, Set.disjoint_image_right, Set.Ioi_disjoint_Iio_of_not_lt, Module.End.eventually_disjoint_ker_pow_range_pow, Function.mulSupport_disjoint_iff, exists_sSupIndep_disjoint_sSup_atoms, exists_open_convex_of_notMem, disjoint_nhds_nhds_iff_not_inseparable, SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, AddAction.isBlock_iff_disjoint_vadd_of_ne, disjoint_nhds_nhdsSet, Matroid.coindep_contract_iff, t2_separation_compact_nhds, IndexedPartition.disjoint, Finset.disjoint_iff_inter_eq_empty, Set.pairwise_disjoint_Ioc_add_intCast, Set.Ico_disjoint_Ico, Filter.not_one_le_div_iff, not_mulDissociated_iff_exists_disjoint, Topology.RelCWComplex.disjointBase, Finset.disjoint_singleton, Finset.subset_sdiff, IsPGroup.le_or_disjoint_of_coprime, Multiset.disjoint_toFinset, Monotone.pairwise_disjoint_on_Ico_pred, isGreatest_compl, t1Space_iff_disjoint_pure_nhds, Multiset.Ico_disjoint_Ico, Metric.disjoint_closedBall_of_lt_infDist, LinearMap.disjoint_ker_iff_injOn, Metric.frontier_thickening_disjoint, MulAction.isBlock_iff_smul_eq_smul_or_disjoint, Finset.disjoint_sup_right, Finset.disjoint_product, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, Submodule.disjoint_span_singleton_of_notMem, mem_codiscreteWithin, Monotone.pairwise_disjoint_on_Ioo_succ, disjoint_sSup_iff, Metric.AreSeparated.disjoint, Set.Ioi_disjoint_Iio_same, Set.mulIndicator_eq_one', BoxIntegral.Box.disjoint_coe, MulAction.IsBlock.disjoint_smul_left, Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite, Finset.supIndep_iff_disjoint_erase, IsLowerSet.disjoint_upperClosure_left, Function.support_disjoint_iff, MulAction.isBlock_iff_disjoint_smul_of_ne, Submodule.isCompl_iff_disjoint, Multiset.disjoint_cons_left, Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependent, IsLocalization.orderIsoOfPrime_symm_apply_coe, Matroid.dual_indep_iff_exists, FreeGroup.startsWith.disjoint_iff_ne, Set.disjoint_vadd_set, disjoint_closedBall_closedBall_iff, Set.one_notMem_inv_mul_iff, Finset.Ioc_disjoint_Ioc_of_le, Finsupp.support_single_disjoint, Set.disjoint_sUnion_right, iSupIndep_def, T2Space.t2, disjoint_pure_nhds, top_disjoint, Set.preimage_eq_empty_iff, Finset.Nonempty.not_disjoint, Set.disjoint_iff_forall_ne, Finset.disjoint_biUnion_left, disjoint_of_le_iff_left_eq_bot, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, Metric.closedBall_disjoint_ball, Equiv.Perm.Disjoint.disjoint_support, IsLocalization.disjoint_comap_iff, Filter.disjoint_atTop_principal_Iic, disjoint_partialSups_left, Finset.supIndep_univ_bool, disjoint_nhds_atTop, AddAction.orbit.eq_or_disjoint, LinearMap.disjoint_ker_of_nondegenerate_restrict, t2Space_iff_nhds, List.pairwise_disjoint_of_coe_toFinset_pairwiseDisjoint, Set.disjoint_image_inl_image_inr, IsLowerSet.disjoint_upperClosure_right, Multiset.disjoint_union_right, Monotone.pairwise_disjoint_on_Ioo_pred, Set.disjoint_sdiff_left, Set.ncard_union_eq_iff, Finset.disjoint_val, Monotone.pairwise_disjoint_on_Ioc_succ, Finset.mem_shadow_iterate_iff_exists_card, Set.pairwise_disjoint_Ico_zpow, Metric.disjoint_cobounded_nhds, sSupIndep_pair, Set.intersecting_insert, Matroid.delete_dep_iff, Set.disjoint_preimage_iff, Filter.HasBasis.disjoint_iff_left, Subgroup.isComplement'_iff_card_mul_and_disjoint, MeasureTheory.exists_subordinate_pairwise_disjoint, Submodule.IsOrtho.disjoint, disjoint_principal_nhdsSet, Multiset.disjoint_cons_right, Matroid.contract_spanning_iff', regularSpace_generateFrom, Set.exists_union_disjoint_cardinal_eq_iff, Filter.one_le_div_iff, le_compl_iff_disjoint_left, le_symmDiff_iff_left, SimpleGraph.IsCompleteBetween.disjoint, Set.disjoint_sdiff_right, Matroid.Indep.contract_indep_iff, UV.disjoint_of_mem_compression_of_notMem, Metric.frontier_cthickening_disjoint, Finset.disjoint_empty_right, Booleanisation.lift_lt_comp, Set.univ_disjoint, Set.Iio_disjoint_Ioi_same, ModuleCat.disjoint_span_sum, Topology.RelCWComplex.disjoint_skeleton_openCell, Finset.disjiUnion_map, Finset.disjoint_insert_left, Finset.exists_disjoint_union_of_even_card_iff, Module.End.generalized_eigenvec_disjoint_range_ker, Set.zero_notMem_sub_iff, Set.one_notMem_div_iff, Filter.disjoint_atTop_atBot, Metric.eball_disjoint, SeminormedGroup.disjoint_nhds_one, Fintype.exists_disjointed_le, Filter.disjoint_prod, regularSpace_iff, MeasureTheory.AEDisjoint.exists_disjoint_diff, Filter.disjoint_atBot_principal_Ioi, disjoint_inf_sdiff, Multiset.zero_disjoint, disjoint_ball_ball_iff, Set.Finite.disjoint_toFinset, LE.le.disjoint_compl_right, Topology.RelCWComplex.disjointBase', Multiset.disjoint_ndinsert_right, Nat.disjoint_primeFactors, AddSubgroup.disjoint_iff_add_eq_zero, SimpleGraph.disjoint_left, disjoint_memPartition, Set.disjoint_empty, NFA.disjoint_stepSet_reverse, Set.disjoint_diagonal_offDiag, Partition.disjoint, sdiff_eq_self_iff_disjoint, PiNat.disjoint_cylinder_of_longestPrefix_lt, IsUpperSet.disjoint_lowerClosure_left, IsUltrametricDist.closedBall_subset_trichotomy, Set.disjoint_vadd_set_left, SimpleGraph.disjoint_image_val_universalVerts, specializes_iff_not_disjoint, ConvexCone.disjoint_hull_right_of_convex, disjoint_compl_right, Set.Ioc_disjoint_Ioc_of_le, Finset.disjoint_right, MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsIn, EMetric.disjoint_closedBall_of_lt_infEdist, MeasureTheory.Measure.MutuallySingular.disjoint_ae, Finset.one_notMem_inv_mul_iff, disjoint_nhds_pure, IsAtom.not_disjoint_iff_le, Set.mulIndicator_eq_one, Ideal.disjoint_primeCompl_of_liesOver, List.pairwiseDisjoint_iff_coe_toFinset_pairwise_disjoint, Multiset.coe_disjoint, Composition.disjoint_range, isCompl_iff', pairwise_disjoint_on_bool, isSeparatedMap_iff_nhds, Set.exists_union_disjoint_ncard_eq_of_even, Set.Ici_disjoint_Iic, Finset.disjoint_sdiff_inter, Set.pairwiseDisjoint_insert, Topology.RelCWComplex.Subcomplex.disjoint_openCell_subcomplex_of_not_mem, Finset.one_notMem_div_iff, Set.one_mem_div_iff, Matroid.delete_isBasis_iff, Finset.disjoint_biUnion_right, Set.pairwise_disjoint_Ico_intCast, disjoint_lift'_closure_nhds, le_compl_iff_disjoint_right, disjoint_disjointed, SimpleGraph.disjoint_sdiff_neighborFinset_image, Set.Iic.isCompl_iff, SimpleGraph.disjoint_fromEdgeSet, sdiff_eq_left, TopologicalSpace.Opens.coe_disjoint, symmDiff_eq_sup, Finset.disjoint_singleton_right, AddSubmonoid.disjoint_def, Finset.powerset_card_disjiUnion, UV.compress_disjoint, Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_inter, PMF.toOuterMeasure_apply_eq_zero_iff, disjoint_sup_left, AddAction.disjoint_image_image_iff, Finset.disjoint_singleton_left, Directed.disjoint_iSup_left, DoubleCoset.disjoint_out, Multiset.disjoint_right, Filter.disjoint_cocompact_right, AddSubgroup.disjoint_def', Finset.disjoint_diag_offDiag, Set.disjoint_vadd_set_right, Set.zero_notMem_neg_add_iff, Set.disjoint_image_inl_range_inr, subsingleton_setOf_mem_iff_pairwise_disjoint, Finset.disjoint_empty_left, Set.Iio_disjoint_Ici, Topology.RelCWComplex.disjoint_skeletonLT_openCell, Filter.disjoint_pure_atBot, Finset.disjoint_box_succ_prod, r1Space_iff_specializes_or_disjoint_nhds, ClosedSubmodule.orthogonal_disjoint, ContinuousMap.exists_disjoint_nonempty_clopen_cover_of_mem_nhds_diagonal, Set.pairwise_disjoint_smul_iff, Finset.disjoint_filter_and_not_filter, symmetric_disjoint, ModelWithCorners.disjoint_interior_boundary, Finset.disjoint_union_left, Set.Ico_disjoint_Ico_same, Nat.Coprime.disjoint_primeFactors, Filter.compl_diagonal_mem_prod, Finset.disjoint_left, Submodule.disjoint_def, Prod.disjoint_iff, CompleteSublattice.disjoint_iff, Submodule.range_ker_disjoint, SubAddAction.disjoint_val_image, UniqueFactorizationMonoid.disjoint_primeFactors, BoxIntegral.Prepartition.disjoint_coe_of_mem, Multiset.disjoint_of_nodup_add, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, MeasureTheory.IsSetSemiring.disjoint_disjointOfDiffUnion, disjoint_iff_inf_le, Antitone.pairwise_disjoint_on_Ico_pred, Matroid.Indep.contract_isBase_iff, MulAction.IsBlock.smul_eq_or_disjoint, Set.zero_mem_sub_iff, Set.Ioo_disjoint_Ioo, Perfect.splitting, Pi.disjoint_iff, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, Metric.sphere_disjoint_ball, Equiv.Perm.ofSubtype_support_disjoint, MvPolynomial.disjoint_support_monomial, RootPairing.disjoint_rootSpan_ker_rootForm, Ideal.exists_disjoint_powers_of_span_eq_top, MeasureTheory.pairwise_disjoint_addFundamentalInterior, Submonoid.disjoint_def', Booleanisation.lift_le_comp, Matroid.Coindep.delete_isBase_iff, pairwise_disjoint_nhds, Set.pairwiseDisjoint_union, Set.disjoint_smul_set_left, disjoint_nhdsWithin_of_mem_discrete, Finset.Ioc_disjoint_Ioc, disjoint_nhds_atTop_iff, MeasureTheory.Measure.MutuallySingular.disjoint, IsCompact.disjoint_nhdsSet_right, Filter.NeBot.not_disjoint, Set.disjoint_smul_set_right, Matroid.dualIndepMatroid_Indep, AddSubgroup.addSubgroupOf_eq_bot, disjoint_self, Filter.HasBasis.disjoint_cobounded_iff, LinearMap.disjoint_ker', PrimeSpectrum.localization_comap_range, IsLocalization.orderIsoOfPrime_apply_coe, Multiset.disjoint_add_right, sdiff_eq_self_iff_disjoint', Filter.disjoint_atBot_principal_Ici, MeasurableSpace.disjoint_countablePartition, NumberField.mixedEmbedding.disjoint_span_commMap_ker, disjoint_of_subsingleton, Metric.disjoint_nhdsSet_cobounded, Heyting.IsRegular.disjoint_compl_left_iff, Set.disjoint_range_inl_image_inr, exists_disjoint_smul_of_isCompact, disjoint_nested_nhds, disjoint_nhdsSet_nhds, Matroid.IsBasis'.contract_dep_iff, Finset.subset_compl_iff_disjoint_left, Matroid.delete_indep_iff, Equiv.Perm.disjoint_iff_disjoint_support, Finset.sdiff_disjoint, Set.pairwise_disjoint_Ico_add_zsmul, Set.disjoint_left_ordSeparatingSet, Submonoid.disjoint_def, Subgroup.disjoint_iff_mul_eq_one, Matroid.Indep.disjoint_loops, Set.Iio_disjoint_Ioi_of_le, Filter.disjoint_pure_atTop, Finsupp.disjoint_supported_supported_iff, Finset.disjoint_range_addRightEmbedding, IsCompl.disjoint, SeminormedAddGroup.disjoint_nhds, disjoint_sdiff_self_left, IsCompl.le_left_iff, IsCompact.disjoint_nhdsSet_nhds, Multiset.add_eq_union_left_of_le, SimpleGraph.singleton_disjoint_neighborFinset, Urysohns.CU.disjoint_C_support_lim, Multiset.ndinter_eq_zero_iff_disjoint, IsUpperSet.disjoint_lowerClosure_right, Finset.zero_notMem_neg_add_iff, Order.Ideal.PrimePair.disjoint, Multiset.add_eq_union_right_of_le, IsLocalization.map_algebraMap_ne_top_iff_disjoint, Finsupp.lmapDomain_disjoint_ker, Set.disjoint_range_iff, iSupIndep_iff_pairwiseDisjoint, SimpleGraph.deleteEdges_eq_self, sup_sdiff_injOn, Matroid.delete_isCircuit_iff, Set.disjoint_iUnionβ‚‚_left, Pi.mulSupport_mulSingle_disjoint, Set.prod_subset_compl_diagonal_iff_disjoint, Multiset.disjoint_list_sum_right, SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem, Set.empty_disjoint, r1_separation, DirectedOn.disjoint_sSup_right, Set.disjoint_union_left, Specializes.not_disjoint, Set.Ico.disjoint_iff, NumberField.InfinitePlace.disjoint_isReal_isComplex, Finset.IsAntichain.disjoint_slice_shadow_falling, Multiset.disjoint_ndinsert_left, Matroid.IsBasis'.contract_indep_iff, Multiset.disjoint_sum_right, Module.End.invtSubmodule.disjoint_iff, disjoint_iSupβ‚‚_iff, Finset.disjiUnion_cons, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, Finset.disjiUnion_Iic_disjointed, disjoint_closedBall_ball_iff, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, Multiset.singleton_disjoint, Multiset.disjoint_iff_ne, IsCompl.disjoint_right_iff, Finset.pairwise_disjoint_powersetCard, disjoint_nhds_atBot, MonoidHom.noncommCoprod_injective, Finset.disjoint_erase_comm, Set.pairwise_disjoint_Ioo_intCast, PiNat.exists_disjoint_cylinder, t2_separation, TopologicalSpace.IsOpenCover.exists_finite_nonempty_disjoint_clopen_cover, LieIdeal.comap_incl_eq_bot, NumberField.mixedEmbedding.disjoint_negAt_plusPart, PMF.toMeasure_apply_eq_zero_iff, IsCompl.disjoint_left_iff, Set.Ioc_disjoint_Ioi_same, Complementeds.disjoint_coe, Multiset.inter_eq_zero_iff_disjoint, Topology.RelCWComplex.disjoint_base_iUnion_openCell, AddAction.IsBlock.vadd_eq_or_disjoint, Submodule.disjoint_iff_comap_eq_bot, mul_eq_mul_prime_prod, Finset.subset_compl_iff_disjoint_right, Multiset.nodup_add, IsUltrametricDist.closedBall_eq_or_disjoint, Concept.disjoint_extent_intent, Function.disjoint_support_iff, pairwise_disjoint_on, LE.le.disjoint_compl_left, Finset.not_disjoint_iff, Finset.disjoint_of_subset_iff_left_eq_empty, Subgroup.IsComplement'.disjoint, Set.disjoint_iff, Set.one_mem_inv_mul_iff, disjoint_nhds_nhds, disjoint_sdiff_sdiff, IsCompl.le_right_iff, Set.Nonempty.not_disjoint, Antitone.pairwise_disjoint_on_Ico_succ, Filter.disjoint_principal_right, Topology.RelCWComplex.disjoint_interior_base_iUnion_closedCell, Metric.closedBall_disjoint_closedBall, t2Space_iff, Submodule.disjoint_span_singleton'', LieModule.disjoint_genWeightSpace, Set.disjoint_univ_pi, Monotone.pairwise_disjoint_on_Ico_succ, Ultrafilter.disjoint_iff_not_le

Theorems

NameKindAssumesProvesValidatesDepends On
iInter_Iic_eq_empty_iff πŸ“–mathematicalβ€”Set.iInter
Set.Iic
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set
Set.instEmptyCollection
BddBelow
Preorder.toLE
Set.range
β€”β€”
iInter_Iio_of_not_bddBelow_range πŸ“–mathematicalBddBelow
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.range
Set.iInter
Set.Iio
Set
Set.instEmptyCollection
β€”Set.eq_empty_of_subset_empty
iInter_Iic_eq_empty_iff
Set.iInter_mono''
Set.Iio_subset_Iic_self
iUnion_Ici_eq_Ici_iInf πŸ“–mathematicalSet
Set.instMembership
Set.range
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompletelyDistribLattice.toCompleteLattice
CompleteLinearOrder.toCompletelyDistribLattice
Set.iUnion
Set.Ici
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
β€”IsGLB.biUnion_Ici_eq_Ici
isGLB_iInf
Set.iUnion_congr_Prop
Set.iUnion_exists
Set.iUnion_iUnion_eq'
iUnion_Ici_eq_Ioi_iInf πŸ“–mathematicalSet
Set.instMembership
Set.range
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompletelyDistribLattice.toCompleteLattice
CompleteLinearOrder.toCompletelyDistribLattice
Set.iUnion
Set.Ici
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
Set.Ioi
β€”IsGLB.biUnion_Ici_eq_Ioi
isGLB_iInf
Set.iUnion_congr_Prop
Set.iUnion_exists
Set.iUnion_iUnion_eq'
iUnion_Iic_eq_Iic_iSup πŸ“–mathematicalSet
Set.instMembership
Set.range
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompletelyDistribLattice.toCompleteLattice
CompleteLinearOrder.toCompletelyDistribLattice
Set.iUnion
Set.Iic
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
β€”iUnion_Ici_eq_Ici_iInf
iUnion_Iic_eq_Iio_iSup πŸ“–mathematicalSet
Set.instMembership
Set.range
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompletelyDistribLattice.toCompleteLattice
CompleteLinearOrder.toCompletelyDistribLattice
Set.iUnion
Set.Iic
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set.Iio
β€”iUnion_Ici_eq_Ioi_iInf
iUnion_Iic_of_not_bddAbove_range πŸ“–mathematicalBddAbove
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.range
Set.iUnion
Set.Iic
Set.univ
β€”Set.eq_univ_of_subset
Set.iUnion_mono''
Set.Iio_subset_Iic_self
iUnion_Iio_eq_univ_iff
iUnion_Iio_eq_univ_iff πŸ“–mathematicalβ€”Set.iUnion
Set.Iio
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.univ
BddAbove
Preorder.toLE
Set.range
β€”β€”

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