Documentation Verification Report

Cofinality

πŸ“ Source: Mathlib/SetTheory/Cardinal/Cofinality.lean

Statistics

MetricCount
Definitionscof, cof
2
TheoremsiSup_lt_of_lt_cof_ord, lift_iSup_lt_of_lt_cof_ord, lt_cof_power, lt_power_cof, mk_bounded_subset, mk_subset_mk_lt_cof, sSup_lt_of_lt_cof_ord, unbounded_of_unbounded_iUnion, unbounded_of_unbounded_sUnion, cof_le, cof_le_lift, aleph0_le_cof_iff, cof_Iio, cof_congr_of_strictMono, cof_eq, cof_eq_aleph0, cof_eq_one, cof_eq_one_iff, cof_eq_zero, cof_eq_zero_iff, cof_int, cof_le, cof_le_cardinalMk, cof_le_one_iff, cof_lt_aleph0_iff, cof_nat, cof_ne_one, cof_ne_one_iff, cof_ne_zero, cof_ne_zero_iff, cof_ord_cof, le_cof, le_cof_iff, le_lift_cof_iff, lift_cof_congr_of_strictMono, one_lt_cof, one_lt_cof_iff, cof_congr, cof_eq, lift_cof_congr, lift_cof_eq, cof_eq, cof_le, aleph0_le_cof, aleph0_le_cof_iff, blsub_lt_ord, blsub_lt_ord_lift, bsup_lt_ord, bsup_lt_ord_lift, cof_Iio, cof_add, cof_add_one, cof_blsub_le, cof_blsub_le_lift, cof_bsup_le, cof_bsup_le_lift, cof_cof, cof_eq, cof_eq', cof_eq_aleph0_of_isSuccLimit, cof_eq_cof_toType, cof_eq_of_isNormal, cof_eq_one_iff, cof_eq_one_iff_is_succ, cof_eq_sInf_lsub, cof_eq_zero, cof_iSup, cof_iSup_Iio, cof_iSup_Iio_add_one, cof_iSup_add_one, cof_iSup_add_one_le, cof_iSup_le, cof_iSup_le_lift, cof_le_card, cof_le_of_isNormal, cof_lift_iSup_add_one_le, cof_lsub_def_nonempty, cof_lsub_le, cof_lsub_le_lift, cof_lt_aleph0_iff, cof_map_of_isNormal, cof_ne_zero, cof_omega, cof_omega0, cof_one, cof_ord_cof, cof_ord_le, cof_pos, cof_preOmega, cof_succ, cof_toType, cof_type, cof_type_le, cof_type_lt, cof_univ, cof_zero, exists_blsub_cof, exists_lsub_cof, iSup_add_one_lt_of_lt_cof, iSup_lt, iSup_lt_lift, iSup_lt_of_lt_cof, iSup_lt_ord, iSup_lt_ord_lift, le_cof_iff_blsub, le_cof_iff_lsub, le_cof_map_of_isNormal, le_cof_type, lift_cof, lift_cof_iSup, lift_cof_iSup_add_one, lift_iSup_add_one_lt_of_lt_cof, lift_iSup_lt_of_lt_cof, lsub_lt_ord, lsub_lt_ord_lift, lt_cof_type, nfpFamily_lt_ord, nfpFamily_lt_ord_lift, nfp_lt_ord, one_lt_cof_iff, ord_cof_eq, ord_cof_le, sSup_add_one_lt_of_lt_cof, sSup_lt_of_lt_cof, cof_eq, cof_eq_lift, isCofinal_of_isCofinal_iUnion, isCofinal_of_isCofinal_sUnion
128
Total130

Cardinal

Theorems

NameKindAssumesProvesValidatesDepends On
iSup_lt_of_lt_cof_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
Ordinal.cof
ord
Cardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”ord_lt_ord
Ordinal.iSup_ord
Ordinal.iSup_lt_of_lt_cof
lift_iSup_lt_of_lt_cof_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
lift
Ordinal.cof
ord
Cardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”ord_lt_ord
Ordinal.iSup_ord
Ordinal.lift_iSup_lt_of_lt_cof
lift_ord
lt_cof_power πŸ“–mathematicalCardinal
instLE
aleph0
Preorder.toLT
PartialOrder.toPreorder
partialOrder
instOne
Cardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
Ordinal.cof
ord
instPowCardinal
β€”LT.lt.ne'
LT.lt.trans
zero_lt_one
IsOrderedRing.toZeroLEOneClass
isOrderedRing
NeZero.charZero_one
instCharZero
lt_imp_lt_of_le_imp_le
power_le_power_left
power_ne_zero
power_mul
mul_eq_self
lt_power_cof
LE.le.trans
LT.lt.le
cantor'
lt_power_cof πŸ“–mathematicalCardinal
instLE
aleph0
Cardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
instPowCardinal
Ordinal.cof
ord
β€”inductionOn
exists_ord_eq
isSuccLimit_ord
Ordinal.cof_eq'
sum_lt_prod
Ordinal.typein_lt_type
lt_ord
lt_of_le_of_lt
prod_const
lift_id
mk_bounded_subset πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
instPowCardinal
instOfNatAtLeastTwo
instNatCast
Nat.instAtLeastTwoHAddOfNat
ord
Ordinal.type
Set
Set.Bounded
β€”Nat.instAtLeastTwoHAddOfNat
eq_or_ne
mk_eq_zero_iff
Set.not_unbounded_iff
Set.unbounded_of_isEmpty
IsStrongLimit.aleph0_le
le_antisymm
Set.setOf_exists
Set.coe_setOf
LE.le.trans
sum_le_mk_mul_iSup
mul_le_max_of_aleph0_le_left
max_eq_left
ciSup_le'
mk_powerset
LT.lt.le
IsStrongLimit.two_power_lt
card_typein_lt
le_refl
mk_le_of_injective
Ordinal.bounded_singleton
isSuccLimit_ord
mk_subset_mk_lt_cof πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
instPowCardinal
instOfNatAtLeastTwo
instNatCast
Nat.instAtLeastTwoHAddOfNat
Set
Cardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
Set.Elem
Ordinal.cof
ord
β€”Nat.instAtLeastTwoHAddOfNat
eq_or_ne
ord_zero
Ordinal.cof_zero
canonicallyOrderedAdd
mk_eq_zero
Subtype.isEmpty_false
exists_ord_eq
le_antisymm
mk_bounded_subset
mk_subtype_le_of_subset
Mathlib.Tactic.Contrapose.contrapose₁
Order.cof_le
instIsStrictTotalOrderOfIsWellOrder
Set.not_bounded_iff
mk_le_of_injective
mk_singleton
Ordinal.one_lt_cof_iff
isSuccLimit_ord
IsStrongLimit.aleph0_le
sSup_lt_of_lt_cof_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
Set.Elem
Ordinal.cof
ord
lift
Cardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”ord_lt_ord
Ordinal.sSup_ord
Ordinal.sSup_lt_of_lt_cof
mk_image_eq
ord_injective
lift_ord
unbounded_of_unbounded_iUnion πŸ“–mathematicalIsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.iUnion
Cardinal
Preorder.toLT
partialOrder
Order.cof
IsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”isCofinal_of_isCofinal_iUnion
unbounded_of_unbounded_sUnion πŸ“–mathematicalIsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.sUnion
Cardinal
Preorder.toLT
partialOrder
Set.Elem
Set
Order.cof
Set
Set.instMembership
IsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”isCofinal_of_isCofinal_sUnion

GaloisConnection

Theorems

NameKindAssumesProvesValidatesDepends On
cof_le πŸ“–mathematicalGaloisConnectionCardinal
Cardinal.instLE
Order.cof
β€”Cardinal.lift_id
cof_le_lift
cof_le_lift πŸ“–mathematicalGaloisConnectionCardinal
Cardinal.instLE
Cardinal.lift
Order.cof
β€”Order.le_lift_cof_iff
LE.le.trans
Cardinal.lift_le
Order.cof_le
map_isCofinal
Cardinal.mk_image_le_lift

Order

Definitions

NameCategoryTheorems
cof πŸ“–CompOp
44 mathmath: cof_eq_one, cof_eq_aleph0, Ordinal.cof_Iio, cof_eq_zero_iff, le_cof, OrderIso.lift_cof_eq, cof_le_one_iff, cof_eq_one_iff, Ordinal.cof_type, Ordinal.lift_cof_iSup_add_one, cof_nat, RelIso.cof_eq, Ordinal.lift_cof_iSup, Ordinal.lt_cof_type, cof_ord_cof, one_lt_cof_iff, Ordinal.cof_iSup, cof_int, cof_Iio, aleph0_le_cof_iff, le_lift_cof_iff, lift_cof_congr_of_strictMono, Ordinal.cof_eq_cof_toType, OrderIso.lift_cof_congr, Ordinal.cof_toType, Ordinal.cof_type_le, cof_eq, cof_congr_of_strictMono, RelIso.cof_eq_lift, Ordinal.ord_cof_eq, cof_eq_zero, one_lt_cof, OrderIso.cof_eq, cof_le, cof_lt_aleph0_iff, Ordinal.cof_type_lt, GaloisConnection.cof_le_lift, Ordinal.cof_eq, Ordinal.cof_iSup_add_one, le_cof_iff, cof_le_cardinalMk, Ordinal.le_cof_type, OrderIso.cof_congr, GaloisConnection.cof_le

Theorems

NameKindAssumesProvesValidatesDepends On
aleph0_le_cof_iff πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
Cardinal.aleph0
cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
Cardinal.partialOrder
Cardinal.instOne
β€”β€”
cof_Iio πŸ“–mathematicalβ€”cof
Set.Elem
Set.Iio
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Subtype.preorder
Set
Set.instMembership
Ordinal.cof
DFunLike.coe
RelEmbedding
Ordinal
Preorder.toLT
Ordinal.partialOrder
RelEmbedding.instFunLike
PrincipalSeg.toRelEmbedding
Ordinal.typein
isWellOrder_lt
β€”isWellOrder_lt
Subtype.wellFoundedLT
Ordinal.cof_type
cof_congr_of_strictMono πŸ“–mathematicalStrictMono
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
IsCofinal
Preorder.toLE
Set.range
cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Cardinal.lift_id
lift_cof_congr_of_strictMono
cof_eq πŸ“–mathematicalβ€”Set
IsCofinal
Preorder.toLE
Set.Elem
cof
β€”ciInf_mem
Cardinal.instWellFoundedLT
cof_eq_aleph0 πŸ“–mathematicalβ€”cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Cardinal.aleph0
β€”LE.le.antisymm
LE.le.trans
cof_le_cardinalMk
Cardinal.mk_le_aleph0
instNoTopOrderOfNoMaxOrder
cof_eq_one πŸ“–mathematicalβ€”cof
Cardinal
Cardinal.instOne
β€”cof_eq_one_iff
isTop_top
cof_eq_one_iff πŸ“–mathematicalβ€”cof
Cardinal
Cardinal.instOne
IsTop
Preorder.toLE
β€”cof_eq
Cardinal.mk_set_eq_one_iff
isCofinal_singleton_iff
le_antisymm
LE.le.trans_eq
cof_le
Cardinal.mk_singleton
Cardinal.one_le_iff_ne_zero
cof_ne_zero_iff
cof_eq_zero πŸ“–mathematicalβ€”cof
Cardinal
Cardinal.instZero
β€”cof_eq_zero_iff
cof_eq_zero_iff πŸ“–mathematicalβ€”cof
Cardinal
Cardinal.instZero
IsEmpty
β€”cof_eq
Cardinal.mk_eq_zero
instIsEmptySubtype
ciInf_const
cof_int πŸ“–mathematicalβ€”cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
instLatticeInt
Cardinal.aleph0
β€”cof_eq_aleph0
LinearOrderedAddCommGroup.to_noMaxOrder
Int.instIsOrderedAddMonoid
Infinite.instNontrivial
Int.infinite
instCountableInt
cof_le πŸ“–mathematicalIsCofinal
Preorder.toLE
Cardinal
Cardinal.instLE
cof
Set.Elem
β€”ciInf_le'
cof_le_cardinalMk πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
β€”LE.le.trans_eq
cof_le
IsCofinal.univ
Cardinal.mk_univ
cof_le_one_iff πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
Cardinal.instOne
IsTop
Preorder.toLE
β€”le_iff_lt_or_eq
Cardinal.lt_one_iff
cof_eq_one_iff
cof_lt_aleph0_iff πŸ“–mathematicalβ€”Cardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Cardinal.aleph0
Cardinal.instLE
Cardinal.instOne
β€”cof_eq
Set.Finite.eq_1
Cardinal.mk_lt_aleph0_iff
Eq.trans_lt
Set.Finite.exists_subsingleton_isCofinal
LE.le.trans
cof_le
lt_of_le_of_lt
Cardinal.one_lt_aleph0
cof_nat πŸ“–mathematicalβ€”cof
Nat.instPreorder
Cardinal.aleph0
β€”cof_eq_aleph0
Nat.instNoMaxOrder
instCountableNat
cof_ne_one πŸ“–β€”β€”β€”β€”cof_ne_one_iff
cof_ne_one_iff πŸ“–mathematicalβ€”NoTopOrder
Preorder.toLE
β€”not_iff_not
noTopOrder_iff
cof_eq_one_iff
cof_ne_zero πŸ“–β€”β€”β€”β€”cof_ne_zero_iff
cof_ne_zero_iff πŸ“–β€”β€”β€”β€”Iff.not
cof_eq_zero_iff
cof_ord_cof πŸ“–mathematicalβ€”Ordinal.cof
Cardinal.ord
cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”isWellOrder_lt
Subtype.wellFoundedLT
Ordinal.ord_cof_eq
Ordinal.cof_type
le_antisymm
Cardinal.card_ord
Ordinal.card_type
cof_le_cardinalMk
le_cof_iff
LE.le.trans_eq
cof_le
IsCofinal.trans
Cardinal.mk_image_eq
Subtype.val_injective
le_cof πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
Set.Elem
β€”le_cof_iff
le_cof_iff πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
Set.Elem
β€”Cardinal.lift_id
le_lift_cof_iff
le_lift_cof_iff πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
Cardinal.lift
cof
Set.Elem
β€”Cardinal.lift_iInf
le_ciInf_iff'
lift_cof_congr_of_strictMono πŸ“–mathematicalStrictMono
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
IsCofinal
Preorder.toLE
Set.range
Cardinal.lift
cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”le_antisymm
le_lift_cof_iff
LE.le.trans
Cardinal.lift_le
cof_le
Set.mem_range_self
StrictMono.le_iff_le
Cardinal.mk_range_le_lift
IsCofinal.image
StrictMono.monotone
Cardinal.mk_image_le_lift
one_lt_cof πŸ“–mathematicalβ€”Cardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.instOne
cof
β€”one_lt_cof_iff
one_lt_cof_iff πŸ“–mathematicalβ€”Cardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.instOne
cof
NoTopOrder
Preorder.toLE
β€”not_iff_not
not_lt
noTopOrder_iff
cof_le_one_iff

OrderIso

Theorems

NameKindAssumesProvesValidatesDepends On
cof_congr πŸ“–mathematicalβ€”Order.cofβ€”Cardinal.lift_id
lift_cof_congr
cof_eq πŸ“–mathematicalβ€”Order.cofβ€”cof_congr
lift_cof_congr πŸ“–mathematicalβ€”Cardinal.lift
Order.cof
β€”LE.le.antisymm
GaloisConnection.cof_le_lift
to_galoisConnection
lift_cof_eq πŸ“–mathematicalβ€”Cardinal.lift
Order.cof
β€”lift_cof_congr

Ordinal

Definitions

NameCategoryTheorems
cof πŸ“–CompOp
76 mathmath: cof_iSup_add_one_le, cof_iSup_le_lift, cof_blsub_le, cof_iSup_Iio, cof_zero, cof_Iio, cof_add_one, cof_eq_one_iff_is_succ, cof_preOmega, cof_type, cof_lsub_le_lift, Cardinal.lt_power_cof, lift_cof_iSup_add_one, IsFundamentalSeq.le_ord_cof, cof_blsub_le_lift, cof_one, aleph0_le_cof_iff, IsNormal.cof_le, lift_cof_iSup, exists_fundamental_sequence, Cardinal.isRegular_cof, cof_map_of_isNormal, Cardinal.lt_cof_power, cof_eq_of_isNormal, cof_add, cof_le_card, Cardinal.cof_omega_one, le_cof_iff_blsub, Cardinal.IsRegular.cof_ord, Cardinal.cof_preOmega_add_one, Order.cof_ord_cof, cof_ord_cof, cof_iSup, cof_succ, cof_eq', Order.cof_Iio, cof_iSup_Iio_add_one, cof_le_of_isNormal, cof_univ, exists_lsub_cof, lift_cof, cof_eq_cof_toType, cof_eq_sInf_lsub, ord_cof_le, Cardinal.mk_subset_mk_lt_cof, cof_toType, cof_lift_iSup_add_one_le, cof_cof, IsFundamentalSeq.ord_cof, Cardinal.IsRegular.cof_omega_eq, aleph0_le_cof, IsFundamentalSequence.ord_cof, IsNormal.cof_eq, cof_pos, cof_ord_le, cof_type_lt, cof_eq_one_iff, Cardinal.IsRegular.cof_eq, cof_eq_zero, cof_lsub_le, cof_bsup_le_lift, cof_lt_aleph0_iff, cof_iSup_add_one, cof_omega, le_cof_map_of_isNormal, le_cof_iff_lsub, exists_blsub_cof, cof_bsup_le, cof_omega0, Cardinal.IsInaccessible.le_cof_ord, cof_eq_aleph0_of_isSuccLimit, cof_iSup_le, Cardinal.cof_omega_add_one, one_lt_cof_iff, Cardinal.IsRegular.le_cof_ord, IsFundamentalSequence.cof_eq

Theorems

NameKindAssumesProvesValidatesDepends On
aleph0_le_cof πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
Cardinal.aleph0
cof
Order.IsSuccLimit
Ordinal
PartialOrder.toPreorder
partialOrder
β€”aleph0_le_cof_iff
one_lt_cof_iff
aleph0_le_cof_iff πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
Cardinal.aleph0
cof
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.instOne
β€”β€”
blsub_lt_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
card
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
blsub
β€”blsub_lt_ord_lift
Cardinal.lift_id
blsub_lt_ord_lift πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
card
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
blsub
β€”lt_of_le_of_ne
blsub_le
LT.lt.not_ge
lift_card
cof_blsub_le_lift
bsup_lt_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
card
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
bsup
β€”bsup_lt_ord_lift
Cardinal.lift_id
bsup_lt_ord_lift πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
card
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
bsup
β€”LE.le.trans_lt
bsup_le_blsub
blsub_lt_ord_lift
cof_Iio πŸ“–mathematicalβ€”Order.cof
Set.Elem
Ordinal
Set.Iio
PartialOrder.toPreorder
partialOrder
Subtype.preorder
Set
Set.instMembership
cof
lift
β€”isWellOrder_lt
wellFoundedLT
Order.cof_Iio
typein_ordinal
cof_add πŸ“–mathematicalβ€”cof
Ordinal
add
β€”zero_or_succ_or_isSuccLimit
Order.succ_eq_add_one
add_assoc
cof_add_one
cof_map_of_isNormal
isNormal_add_right
cof_add_one πŸ“–mathematicalβ€”cof
Ordinal
add
one
Cardinal
Cardinal.instOne
β€”cof_eq_one_iff
Set.mem_range_self
cof_blsub_le πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
blsub
card
β€”Cardinal.lift_id
cof_blsub_le_lift
cof_blsub_le_lift πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
blsub
Cardinal.lift
card
β€”Cardinal.mk_toType
cof_lsub_le_lift
type_toType
cof_bsup_le πŸ“–mathematicalOrdinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
bsup
Cardinal
Cardinal.instLE
cof
bsup
card
β€”Cardinal.lift_id
cof_bsup_le_lift
cof_bsup_le_lift πŸ“–mathematicalOrdinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
bsup
Cardinal
Cardinal.instLE
cof
bsup
Cardinal.lift
card
β€”bsup_eq_blsub_iff_lt_bsup
cof_blsub_le_lift
cof_cof πŸ“–mathematicalβ€”cof
Cardinal.ord
β€”cof_ord_cof
cof_eq πŸ“–mathematicalβ€”Set
IsCofinal
Preorder.toLE
Set.Elem
Order.cof
β€”Order.cof_eq
cof_eq' πŸ“–mathematicalOrder.IsSuccLimit
Ordinal
PartialOrder.toPreorder
partialOrder
type
Set
Set.instMembership
Set.Elem
cof
type
β€”instIsStrictTotalOrderOfIsWellOrder
IsWellOrder.toIsWellFounded
isWellOrder_lt
isSuccPrelimit_type_lt_iff
Order.IsSuccLimit.isSuccPrelimit
Order.cof_eq
not_bddAbove_iff
not_bddAbove_iff_isCofinal
cof_eq_aleph0_of_isSuccLimit πŸ“–mathematicalOrder.IsSuccLimit
Ordinal
PartialOrder.toPreorder
partialOrder
Preorder.toLT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
omega
one
cof
Cardinal.aleph0
β€”LE.le.antisymm
LE.le.trans
cof_le_card
Cardinal.card_le_iff
Cardinal.succ_aleph0
Cardinal.ord_aleph
aleph0_le_cof_iff
one_lt_cof_iff
cof_eq_cof_toType πŸ“–mathematicalβ€”Order.cof
ToType
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
linearOrder_toType
cof
β€”cof_toType
cof_eq_of_isNormal πŸ“–mathematicalOrder.IsNormal
Ordinal
instLinearOrder
Order.IsSuccLimit
PartialOrder.toPreorder
partialOrder
cofβ€”cof_map_of_isNormal
cof_eq_one_iff πŸ“–mathematicalβ€”cof
Cardinal
Cardinal.instOne
Ordinal
Set
Set.instMembership
Set.range
Order.succ
PartialOrder.toPreorder
partialOrder
instSuccOrder
β€”inductionOnWellOrder
isWellOrder_lt
cof_type
Order.cof_eq_one_iff
type_lt_mem_range_succ_iff
SemilatticeSup.instIsDirectedOrder
cof_eq_one_iff_is_succ πŸ“–mathematicalβ€”cof
Cardinal
Cardinal.instOne
Ordinal
Set
Set.instMembership
Set.range
Order.succ
PartialOrder.toPreorder
partialOrder
instSuccOrder
β€”cof_eq_one_iff
cof_eq_sInf_lsub πŸ“–mathematicalβ€”cof
InfSet.sInf
Cardinal
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
Cardinal.instConditionallyCompleteLinearOrderBot
setOf
Ordinal
lsub
β€”le_antisymm
le_csInf
cof_lsub_def_nonempty
isWellOrder_lt
wellFoundedLT_toType
type_toType
cof_type
LE.le.trans
Order.cof_le
typein_lt_self
lt_lsub
Set.mem_preimage
typein_enum
Set.mem_range_self
not_lt
typein_le_typein
Cardinal.mk_le_of_injective
Subtype.prop
csInf_le'
Order.cof_eq
lsub_le
le_of_forall_lt
LE.le.trans_lt
cof_toType
cof_eq_zero πŸ“–mathematicalβ€”cof
Cardinal
Cardinal.instZero
Ordinal
zero
β€”cof_toType
Order.cof_eq_zero_iff
isEmpty_toType_iff
cof_iSup πŸ“–mathematicalStrictMono
Ordinal
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
partialOrder
cof
iSup
Ordinal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
Order.cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Cardinal.lift_id
lift_cof_iSup
UnivLE.small
UnivLE.self
cof_iSup_Iio πŸ“–mathematicalStrictMono
Set.Elem
Ordinal
Set.Iio
PartialOrder.toPreorder
partialOrder
Subtype.preorder
Set
Set.instMembership
Order.IsSuccPrelimit
Preorder.toLT
cof
iSup
Ordinal
Set.Elem
Set.Iio
PartialOrder.toPreorder
partialOrder
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”iSup_Iio_add_one
cof_iSup_Iio_add_one
cof_iSup_Iio_add_one πŸ“–mathematicalStrictMono
Set.Elem
Ordinal
Set.Iio
PartialOrder.toPreorder
partialOrder
Subtype.preorder
Set
Set.instMembership
cof
iSup
Ordinal
Set.Elem
Set.Iio
PartialOrder.toPreorder
partialOrder
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
add
one
β€”cof_Iio
Cardinal.lift_lift
lift_cof_iSup_add_one
small_Iio
cof_iSup_add_one πŸ“–mathematicalStrictMono
Ordinal
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
partialOrder
cof
iSup
Ordinal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
add
one
Order.cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Cardinal.lift_id
lift_cof_iSup_add_one
UnivLE.small
UnivLE.self
cof_iSup_add_one_le πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
iSup
Ordinal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
add
one
β€”lift_id
Cardinal.lift_id
cof_lift_iSup_add_one_le
UnivLE.small
UnivLE.self
cof_iSup_le πŸ“–mathematicalOrdinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
Cardinal
Cardinal.instLE
cof
iSup
Ordinal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”Cardinal.lift_id
cof_iSup_le_lift
cof_iSup_le_lift πŸ“–mathematicalOrdinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
Cardinal
Cardinal.instLE
cof
iSup
Ordinal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
Cardinal.lift
β€”iSup_eq_lsub_iff_lt_iSup
cof_lsub_le_lift
cof_le_card πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
card
β€”cof_toType
Cardinal.mk_toType
Order.cof_le_cardinalMk
cof_le_of_isNormal πŸ“–mathematicalOrder.IsNormal
Ordinal
instLinearOrder
Cardinal
Cardinal.instLE
cof
β€”le_cof_map_of_isNormal
cof_lift_iSup_add_one_le πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
lift
iSup
Ordinal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
add
one
Cardinal.lift
β€”LT.lt.false
lift_iSup_add_one_lt_of_lt_cof
lt_iSup_add_one
cof_lsub_def_nonempty πŸ“–mathematicalβ€”Set.Nonempty
Cardinal
setOf
Ordinal
lsub
β€”β€”
cof_lsub_le πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
lsub
β€”cof_eq_sInf_lsub
csInf_le'
cof_lsub_le_lift πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
lsub
Cardinal.lift
β€”Cardinal.mk_uLift
lsub_eq_of_range_eq
Set.ext
cof_lsub_le
cof_lt_aleph0_iff πŸ“–mathematicalβ€”Cardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Cardinal.aleph0
Cardinal.instLE
Cardinal.instOne
β€”cof_toType
Order.cof_lt_aleph0_iff
cof_map_of_isNormal πŸ“–mathematicalOrder.IsNormal
Ordinal
instLinearOrder
Order.IsSuccLimit
PartialOrder.toPreorder
partialOrder
cofβ€”Order.IsNormal.apply_of_isSuccLimit
cof_iSup_Iio
StrictMono.comp
Order.IsNormal.strictMono
Subtype.strictMono_coe
Order.IsSuccLimit.isSuccPrelimit
cof_ne_zero πŸ“–β€”β€”β€”β€”Iff.not
cof_eq_zero
cof_omega πŸ“–mathematicalOrder.IsSuccLimit
Ordinal
PartialOrder.toPreorder
partialOrder
cof
DFunLike.coe
OrderEmbedding
Ordinal
Preorder.toLE
PartialOrder.toPreorder
partialOrder
instFunLikeOrderEmbedding
omega
β€”cof_map_of_isNormal
isNormal_omega
cof_omega0 πŸ“–mathematicalβ€”cof
omega0
Cardinal.aleph0
β€”cof_eq_aleph0_of_isSuccLimit
isSuccLimit_omega0
omega0_lt_omega_one
cof_one πŸ“–mathematicalβ€”cof
Ordinal
one
Cardinal
Cardinal.instOne
β€”zero_add
cof_add_one
cof_ord_cof πŸ“–mathematicalβ€”cof
Cardinal.ord
β€”cof_toType
Order.cof_ord_cof
wellFoundedLT_toType
cof_ord_le πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
Cardinal.ord
β€”Cardinal.card_ord
cof_le_card
cof_pos πŸ“–mathematicalβ€”Cardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.instZero
cof
Ordinal
partialOrder
zero
β€”Cardinal.canonicallyOrderedAdd
canonicallyOrderedAdd
cof_preOmega πŸ“–mathematicalOrder.IsSuccPrelimit
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
cof
DFunLike.coe
OrderEmbedding
Ordinal
Preorder.toLE
PartialOrder.toPreorder
partialOrder
instFunLikeOrderEmbedding
preOmega
β€”IsMin.eq_bot
bot_eq_zero'
canonicallyOrderedAdd
preOmega_zero
cof_zero
cof_map_of_isNormal
isNormal_preOmega
cof_succ πŸ“–mathematicalβ€”cof
Order.succ
Ordinal
PartialOrder.toPreorder
partialOrder
instSuccOrder
Cardinal
Cardinal.instOne
β€”cof_add_one
cof_toType πŸ“–mathematicalβ€”Order.cof
ToType
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
linearOrder_toType
cof
β€”isWellOrder_lt
wellFoundedLT_toType
type_toType
cof_type
cof_type πŸ“–mathematicalβ€”cof
type
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
IsWellOrder
isWellOrder_lt
Order.cof
β€”liftOnWellOrder_type
cof_type_le πŸ“–mathematicalIsCofinal
Preorder.toLE
Cardinal
Cardinal.instLE
Order.cof
Set.Elem
β€”Order.cof_le
cof_type_lt πŸ“–mathematicalβ€”cof
type
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
IsWellOrder
isWellOrder_lt
Order.cof
β€”cof_type
cof_univ πŸ“–mathematicalβ€”cof
univ
Cardinal.univ
β€”LE.le.antisymm
cof_le_card
cof_type
wellFoundedLT
instNoMaxOrder
Cardinal.mk_le_of_injective
OrderIso.injective
cof_zero πŸ“–mathematicalβ€”cof
Ordinal
zero
Cardinal
Cardinal.instZero
β€”cof_eq_zero
exists_blsub_cof πŸ“–mathematicalβ€”blsub
Cardinal.ord
cof
β€”exists_lsub_cof
Cardinal.exists_ord_eq
blsub_eq_lsub'
exists_lsub_cof πŸ“–mathematicalβ€”lsub
cof
β€”cof_eq_sInf_lsub
csInf_mem
Cardinal.instWellFoundedLT
cof_lsub_def_nonempty
iSup_add_one_lt_of_lt_cof πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
add
one
β€”lift_iSup_add_one_lt_of_lt_cof
lift_cof
Cardinal.lift_lt
iSup_lt πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Cardinal.ord
Cardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
Cardinal.instConditionallyCompleteLinearOrderBot
β€”iSup_lt_lift
Cardinal.lift_id
iSup_lt_lift πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
cof
Cardinal.ord
Cardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
Cardinal.instConditionallyCompleteLinearOrderBot
β€”Cardinal.ord_lt_ord
iSup_ord
iSup_lt_ord_lift
iSup_lt_of_lt_cof πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”lift_iSup_lt_of_lt_cof
lift_cof
Cardinal.lift_lt
iSup_lt_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”iSup_lt_ord_lift
Cardinal.lift_id
iSup_lt_ord_lift πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”LE.le.trans_lt
iSup_le_lsub
lsub_lt_ord_lift
le_cof_iff_blsub πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
card
β€”le_cof_iff_lsub
Cardinal.mk_toType
type_toType
Cardinal.exists_ord_eq
blsub_eq_lsub'
le_cof_iff_lsub πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
cof
β€”cof_eq_sInf_lsub
le_csInf_iff''
cof_lsub_def_nonempty
le_cof_map_of_isNormal πŸ“–mathematicalOrder.IsNormal
Ordinal
instLinearOrder
Cardinal
Cardinal.instLE
cof
β€”zero_or_succ_or_isSuccLimit
cof_zero
zero_le
Cardinal.canonicallyOrderedAdd
cof_succ
Cardinal.one_le_iff_ne_zero
Iff.ne
cof_eq_zero
pos_iff_ne_zero
canonicallyOrderedAdd
LE.le.trans_lt
Order.IsNormal.strictMono
Order.lt_succ
instNoMaxOrder
cof_map_of_isNormal
le_refl
le_cof_type πŸ“–mathematicalβ€”Cardinal
Cardinal.instLE
Order.cof
Set.Elem
β€”Order.le_cof_iff
lift_cof πŸ“–mathematicalβ€”Cardinal.lift
cof
lift
β€”inductionOnWellOrder
isWellOrder_lt
cof_type
instWellFoundedLTULift
type_lt_ulift
Cardinal.lift_id'
Cardinal.lift_umax
OrderIso.lift_cof_congr
lift_cof_iSup πŸ“–mathematicalStrictMono
Ordinal
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
partialOrder
Cardinal.lift
cof
iSup
Ordinal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
Order.cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”iSup_add_one
lift_cof_iSup_add_one
lift_cof_iSup_add_one πŸ“–mathematicalStrictMono
Ordinal
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
partialOrder
Cardinal.lift
cof
iSup
Ordinal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
add
one
Order.cof
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Set.mem_Iio
LT.lt.trans_le
lt_add_one
instZeroLEOneClass
instNeZeroOne
instAddLeftStrictMono
le_ciSup
bddAbove_of_small
small_range
Order.lift_cof_congr_of_strictMono
lt_iSup_add_one_iff
Set.mem_range_self
Cardinal.lift_lift
Cardinal.lift_umax
lift_cof
lift_lift
cof_Iio
lift_iSup_add_one_lt_of_lt_cof πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
cof
lift
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
add
one
β€”iSup.eq_1
Set.range_comp'
sSup_add_one_lt_of_lt_cof
Cardinal.lift_lt
LE.le.trans_lt
Cardinal.mk_range_le_lift
Cardinal.lift_lift
lift_iSup_lt_of_lt_cof πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
cof
lift
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”LE.le.trans_lt
iSup_le_iSup_add_one
lift_iSup_add_one_lt_of_lt_cof
lsub_lt_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
lsub
β€”lsub_lt_ord_lift
Cardinal.lift_id
lsub_lt_ord_lift πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
lsub
β€”lt_of_le_of_ne
lsub_le
LE.le.not_gt
cof_lsub_le_lift
lt_cof_type πŸ“–mathematicalIsCofinal
Preorder.toLE
Cardinal
Cardinal.instLE
Order.cof
Set.Elem
β€”Order.cof_le
nfpFamily_lt_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.aleph0
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
nfpFamily
β€”nfpFamily_lt_ord_lift
Cardinal.lift_id
nfpFamily_lt_ord_lift πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.aleph0
cof
Cardinal.lift
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
nfpFamily
β€”iSup_lt_ord_lift
LE.le.trans_lt
Cardinal.lift_le
Cardinal.mk_list_le_max
Cardinal.lift_max
max_lt
Cardinal.lift_aleph0
nfp_lt_ord πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.aleph0
cof
Ordinal
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
nfp
β€”nfpFamily_lt_ord_lift
Cardinal.mk_fintype
Fintype.card_unique
Nat.cast_one
Cardinal.lift_one
LT.lt.trans
Cardinal.one_lt_aleph0
one_lt_cof_iff πŸ“–mathematicalβ€”Cardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.instOne
cof
Order.IsSuccLimit
Ordinal
partialOrder
β€”not_iff_not
not_lt
Cardinal.le_one_iff
isSuccLimit_iff
not_and_or
not_ne_iff
Order.not_isSuccPrelimit_iff'
instNoMaxOrder
cof_eq_zero
cof_eq_one_iff
ord_cof_eq πŸ“–mathematicalβ€”Set
IsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
type
Set.Elem
Preorder.toLT
Set.instMembership
IsWellOrder
isWellOrder_lt
Subtype.instLinearOrder
Subtype.wellFoundedLT
LinearOrder.toPartialOrder
Cardinal.ord
Order.cof
β€”isWellOrder_lt
Subtype.wellFoundedLT
Order.cof_eq
Cardinal.exists_ord_eq
IsCofinal.trans
isCofinal_setOf_imp_lt
IsWellOrder.toIsWellFounded
LE.le.antisymm'
Cardinal.ord_le
Order.cof_le
type_le_iff'
instTrichotomousLt
instAsymmOfIsWellFounded
trichotomous_of
IsWellOrder.toTrichotomous
LT.lt.asymm
ord_cof_le πŸ“–mathematicalβ€”Ordinal
Preorder.toLE
PartialOrder.toPreorder
partialOrder
Cardinal.ord
cof
β€”LE.le.trans
Cardinal.ord_le_ord
cof_le_card
Cardinal.ord_card_le
sSup_add_one_lt_of_lt_cof πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Set.Elem
Ordinal
cof
lift
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
Set.image
add
one
β€”isWellOrder_lt
Subtype.wellFoundedLT
wellFoundedLT
small_of_injective
small_Iio
EquivLike.toEmbeddingLike
Set.range_comp'
OrderIso.range_eq
Set.image_univ
Subtype.range_coe_subtype
Set.range_comp
sSup_range
lt_of_le_of_ne
instNoMaxOrder
LT.lt.not_ge
Cardinal.lift_lt
Cardinal.lift_lift
cof_type
lift_cof
cof_Iio
lift_cof_iSup_add_one
Order.cof_le_cardinalMk
sSup_lt_of_lt_cof πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Set.Elem
Ordinal
cof
lift
partialOrder
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
β€”LE.le.trans_lt
sSup_le_sSup_add_one
sSup_add_one_lt_of_lt_cof

Ordinal.IsNormal

Theorems

NameKindAssumesProvesValidatesDepends On
cof_eq πŸ“–mathematicalOrder.IsNormal
Ordinal
Ordinal.instLinearOrder
Order.IsSuccLimit
PartialOrder.toPreorder
Ordinal.partialOrder
Ordinal.cofβ€”Ordinal.cof_eq_of_isNormal
cof_le πŸ“–mathematicalOrder.IsNormal
Ordinal
Ordinal.instLinearOrder
Cardinal
Cardinal.instLE
Ordinal.cof
β€”Ordinal.le_cof_map_of_isNormal

RelIso

Theorems

NameKindAssumesProvesValidatesDepends On
cof_eq πŸ“–mathematicalβ€”Order.cofβ€”OrderIso.cof_congr
cof_eq_lift πŸ“–mathematicalβ€”Cardinal.lift
Order.cof
β€”OrderIso.lift_cof_congr

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
isCofinal_of_isCofinal_iUnion πŸ“–mathematicalIsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.iUnion
Cardinal
Preorder.toLT
Cardinal.partialOrder
Order.cof
IsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”isCofinal_of_isCofinal_sUnion
Set.sUnion_range
LE.le.trans_lt
Cardinal.mk_range_le
isCofinal_of_isCofinal_sUnion πŸ“–mathematicalIsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.sUnion
Cardinal
Preorder.toLT
Cardinal.partialOrder
Set.Elem
Set
Order.cof
Set
Set.instMembership
IsCofinal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Mathlib.Tactic.Contrapose.contrapose₁
Mathlib.Tactic.Push.not_and_eq
LE.le.trans
Order.cof_le
LT.lt.le
Cardinal.mk_range_le

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