Documentation Verification Report

Cofinality

📁 Source: Mathlib/SetTheory/Cardinal/Cofinality.lean

Statistics

MetricCount
Definitionscof, IsFundamentalSequence, cof
3
Theoremslt_cof_power, lt_power_cof, mk_bounded_subset, mk_subset_mk_lt_cof, unbounded_of_unbounded_iUnion, unbounded_of_unbounded_sUnion, cof_le, le_cof, blsub_eq, cof_eq, id_of_le_cof, lt, monotone, of_isNormal, ord_cof, strict_mono, succ, trans, zero, cof_eq, cof_le, isFundamentalSequence, aleph0_le_cof, blsub_lt_ord, blsub_lt_ord_lift, bsup_lt_ord, bsup_lt_ord_lift, cof_add, cof_blsub_le, cof_blsub_le_lift, cof_bsup_le, cof_bsup_le_lift, cof_cof, cof_eq, cof_eq', cof_eq_cof_toType, cof_eq_of_isNormal, cof_eq_one_iff_is_succ, cof_eq_sInf_lsub, cof_eq_zero, cof_iSup_le, cof_iSup_le_lift, cof_le_card, cof_le_of_isNormal, cof_lsub_def_nonempty, cof_lsub_le, cof_lsub_le_lift, cof_ne_zero, cof_omega, cof_omega0, cof_ord_le, cof_preOmega, cof_succ, cof_type, cof_type_le, cof_type_lt, cof_univ, cof_zero, exists_blsub_cof, exists_fundamental_sequence, exists_lsub_cof, iSup_lt, iSup_lt_lift, iSup_lt_ord, iSup_lt_ord_lift, le_cof_iff_blsub, le_cof_iff_lsub, le_cof_type, lift_cof, lsub_lt_ord, lsub_lt_ord_lift, lt_cof_type, nfpFamily_lt_ord, nfpFamily_lt_ord_lift, nfp_lt_ord, ord_cof_eq, ord_cof_le, cof_eq, cof_eq_lift
79
Total82

Cardinal

Theorems

NameKindAssumesProvesValidatesDepends On
lt_cof_power 📖mathematicalCardinal
instLE
aleph0
Preorder.toLT
PartialOrder.toPreorder
partialOrder
instOne
Ordinal.cof
ord
instPowCardinal
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 📖mathematicalCardinal
instLE
aleph0
Preorder.toLT
PartialOrder.toPreorder
partialOrder
instPowCardinal
Ordinal.cof
ord
inductionOn
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 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
instPowCardinal
instOfNatAtLeastTwo
instNatCast
Nat.instAtLeastTwoHAddOfNat
ord
Ordinal.type
Set
Set.Bounded
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
Ordinal.card_typein
lt_ord
Ordinal.typein_lt_type
le_refl
mk_le_of_injective
Ordinal.bounded_singleton
isSuccLimit_ord
mk_subset_mk_lt_cof 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
instPowCardinal
instOfNatAtLeastTwo
instNatCast
Nat.instAtLeastTwoHAddOfNat
Set
Set.Elem
Ordinal.cof
ord
Nat.instAtLeastTwoHAddOfNat
eq_or_ne
ord_zero
Ordinal.cof_zero
canonicallyOrderedAdd
mk_eq_zero
Subtype.isEmpty_false
ord_eq
le_antisymm
mk_bounded_subset
mk_le_mk_of_subset
Ordinal.lt_cof_type
mk_le_of_injective
mk_singleton
LT.lt.trans_le
one_lt_aleph0
Ordinal.aleph0_le_cof
isSuccLimit_ord
IsStrongLimit.aleph0_le
unbounded_of_unbounded_iUnion 📖Set.Unbounded
Set.iUnion
Cardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
Order.cof
Function.swap
Compl.compl
Pi.instCompl
Prop.instCompl
unbounded_of_unbounded_sUnion
Set.sUnion_range
LE.le.trans_lt
mk_range_le
unbounded_of_unbounded_sUnion 📖mathematicalSet.Unbounded
Set.sUnion
Cardinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
Set.Elem
Set
Order.cof
Function.swap
Compl.compl
Pi.instCompl
Prop.instCompl
Set.instMembershipIsWellFounded.wf
IsWellOrder.toIsWellFounded
Mathlib.Tactic.Push.not_and_eq
LT.lt.not_ge
le_trans
csInf_le'
Set.mem_range_self
IsWellOrder.toIsTrans
WellFounded.lt_sup
mk_range_le

Order

Definitions

NameCategoryTheorems
cof 📖CompOp
7 mathmath: le_cof, Ordinal.cof_type, RelIso.cof_eq, Ordinal.cof_eq_cof_toType, RelIso.cof_eq_lift, cof_le, Ordinal.cof_type_lt

Theorems

NameKindAssumesProvesValidatesDepends On
cof_le 📖mathematicalSet
Set.instMembership
Cardinal
Cardinal.instLE
cof
Set.Elem
csInf_le'
le_cof 📖mathematicalCardinal
Cardinal.instLE
cof
Set.Elem
cof.eq_1
le_csInf_iff''

Ordinal

Definitions

NameCategoryTheorems
IsFundamentalSequence 📖MathDef
4 mathmath: IsFundamentalSequence.id_of_le_cof, exists_fundamental_sequence, IsFundamentalSequence.succ, IsFundamentalSequence.zero
cof 📖CompOp
49 mathmath: cof_iSup_le_lift, cof_blsub_le, cof_zero, cof_eq_one_iff_is_succ, cof_preOmega, cof_type, cof_lsub_le_lift, Cardinal.lt_power_cof, cof_blsub_le_lift, IsNormal.cof_le, exists_fundamental_sequence, Cardinal.isRegular_cof, Cardinal.lt_cof_power, cof_eq_of_isNormal, cof_add, cof_le_card, le_cof_iff_blsub, cof_succ, cof_eq', 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_cof, cof_type_le, ord_cof_eq, Cardinal.IsRegular.cof_omega_eq, aleph0_le_cof, IsFundamentalSequence.ord_cof, IsNormal.cof_eq, cof_ord_le, cof_type_lt, cof_eq, Cardinal.IsRegular.cof_eq, cof_eq_zero, cof_lsub_le, cof_bsup_le_lift, cof_omega, le_cof_iff_lsub, exists_blsub_cof, cof_bsup_le, cof_omega0, cof_iSup_le, le_cof_type, IsFundamentalSequence.cof_eq

Theorems

NameKindAssumesProvesValidatesDepends On
aleph0_le_cof 📖mathematicalCardinal
Cardinal.instLE
Cardinal.aleph0
cof
Order.IsSuccLimit
Ordinal
PartialOrder.toPreorder
partialOrder
zero_or_succ_or_isSuccLimit
cof_zero
Cardinal.canonicallyOrderedAdd
cof_succ
instNoMaxOrder
le_of_not_gt
Cardinal.lt_aleph0
cof_cof
Order.IsSuccLimit.ne_bot
bot_eq_zero'
canonicallyOrderedAdd
Nat.cast_zero
Cardinal.ord_nat
cof_eq_one_iff_is_succ
natCast_succ
Order.not_isSuccLimit_succ
blsub_lt_ord 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
card
cof
Ordinal
partialOrder
blsubblsub_lt_ord_lift
Cardinal.lift_id
blsub_lt_ord_lift 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
card
cof
Ordinal
partialOrder
blsublt_of_le_of_ne
blsub_le
LT.lt.not_ge
lift_card
cof_blsub_le_lift
bsup_lt_ord 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
card
cof
Ordinal
partialOrder
bsupbsup_lt_ord_lift
Cardinal.lift_id
bsup_lt_ord_lift 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
card
cof
Ordinal
partialOrder
bsupLE.le.trans_lt
bsup_le_blsub
blsub_lt_ord_lift
cof_add 📖mathematicalcof
Ordinal
add
zero_or_succ_or_isSuccLimit
add_succ
cof_succ
cof_eq_of_isNormal
isNormal_add_right
cof_blsub_le 📖mathematicalCardinal
Cardinal.instLE
cof
blsub
card
Cardinal.lift_id
cof_blsub_le_lift
cof_blsub_le_lift 📖mathematicalCardinal
Cardinal.instLE
cof
blsub
Cardinal.lift
card
Cardinal.mk_toType
cof_lsub_le_lift
type_toType
cof_bsup_le 📖mathematicalOrdinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
bsup
Cardinal
Cardinal.instLE
cof
card
Cardinal.lift_id
cof_bsup_le_lift
cof_bsup_le_lift 📖mathematicalOrdinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
bsup
Cardinal
Cardinal.instLE
cof
Cardinal.lift
card
bsup_eq_blsub_iff_lt_bsup
cof_blsub_le_lift
cof_cof 📖mathematicalcof
Cardinal.ord
exists_fundamental_sequence
Cardinal.ord_injective
IsFundamentalSequence.cof_eq
IsFundamentalSequence.trans
cof_eq 📖mathematicalSet.Unbounded
Set.Elem
cof
type
csInf_mem
Cardinal.instWellFoundedLT
Std.Refl.swap
Std.Irrefl.compl
IsStrictOrder.toIrrefl
IsStrictTotalOrder.toIsStrictOrder
instIsStrictTotalOrderOfIsWellOrder
cof_eq' 📖mathematicalOrder.IsSuccLimit
Ordinal
PartialOrder.toPreorder
partialOrder
type
Set
Set.instMembership
Set.Elem
cof
cof_eq
Order.IsSuccLimit.succ_lt
typein_lt_type
IsOrderConnected.conn
isStrictOrderConnected_of_isStrictTotalOrder
instIsStrictTotalOrderOfIsWellOrder
typein_lt_typein
typein_enum
Order.lt_succ
instNoMaxOrder
cof_eq_cof_toType 📖mathematicalcof
Order.cof
ToType
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
linearOrder_toType
isWellOrder_lt
wellFoundedLT_toType
type_toType
cof_type_lt
cof_eq_of_isNormal 📖mathematicalOrder.IsNormal
Ordinal
instLinearOrder
Order.IsSuccLimit
PartialOrder.toPreorder
partialOrder
cofexists_fundamental_sequence
Cardinal.ord_injective
IsFundamentalSequence.cof_eq
IsFundamentalSequence.of_isNormal
cof_eq_one_iff_is_succ 📖mathematicalcof
Cardinal
Cardinal.instOne
Order.succ
Ordinal
PartialOrder.toPreorder
partialOrder
instSuccOrder
inductionOn
cof_eq
Cardinal.mk_ne_zero_iff
one_ne_zero
NeZero.charZero_one
Cardinal.instCharZero
Sum.instIsWellOrderLex
instIsWellOrderEmptyRelationOfSubsingleton
Sum.instTrichotomousLex_mathlib
Subrel.instTrichotomousSubtype
IsWellOrder.toTrichotomous
instAsymmOfIsWellFounded
IsWellOrder.toIsWellFounded
instIsEmptyFalse
trichotomous_of
Cardinal.le_one_iff_subsingleton
le_of_eq
Lean.Meta.FastSubsingleton.elim
cof_succ
cof_eq_sInf_lsub 📖mathematicalcof
InfSet.sInf
Cardinal
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
Cardinal.instConditionallyCompleteLinearOrderBot
setOf
Ordinal
lsub
le_antisymm
le_csInf
cof_lsub_def_nonempty
isWellOrder_lt
wellFoundedLT_toType
type_toType
LE.le.trans
cof_type_le
typein_lt_self
lt_lsub
Set.mem_preimage
typein_enum
Set.mem_range_self
typein_le_typein
Cardinal.mk_le_of_injective
Subtype.prop
csInf_le'
cof_eq
lsub_le
le_of_forall_lt
LE.le.trans_lt
cof_eq_zero 📖mathematicalcof
Cardinal
Cardinal.instZero
Ordinal
zero
inductionOn
cof_eq
type_eq_zero_iff_isEmpty
Cardinal.mk_eq_zero_iff
cof_zero
cof_iSup_le 📖mathematicalOrdinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
Cardinal
Cardinal.instLE
cof
Cardinal.lift_id
cof_iSup_le_lift
cof_iSup_le_lift 📖mathematicalOrdinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
Cardinal
Cardinal.instLE
cof
Cardinal.lift
iSup_eq_lsub_iff_lt_iSup
cof_lsub_le_lift
cof_le_card 📖mathematicalCardinal
Cardinal.instLE
cof
card
cof_eq_sInf_lsub
csInf_le'
cof_le_of_isNormal 📖mathematicalOrder.IsNormal
Ordinal
instLinearOrder
Cardinal
Cardinal.instLE
cof
zero_or_succ_or_isSuccLimit
cof_zero
zero_le
Cardinal.canonicallyOrderedAdd
cof_succ
Cardinal.one_le_iff_ne_zero
cof_ne_zero
pos_iff_ne_zero
canonicallyOrderedAdd
LE.le.trans_lt
Order.IsNormal.strictMono
Order.lt_succ
instNoMaxOrder
cof_eq_of_isNormal
le_refl
cof_lsub_def_nonempty 📖mathematicalSet.Nonempty
Cardinal
setOf
Ordinal
lsub
cof_lsub_le 📖mathematicalCardinal
Cardinal.instLE
cof
lsub
cof_eq_sInf_lsub
csInf_le'
cof_lsub_le_lift 📖mathematicalCardinal
Cardinal.instLE
cof
lsub
Cardinal.lift
Cardinal.mk_uLift
lsub_eq_of_range_eq
Set.ext
cof_lsub_le
cof_ne_zero 📖Iff.not
cof_eq_zero
cof_omega 📖mathematicalOrder.IsSuccLimit
Ordinal
PartialOrder.toPreorder
partialOrder
cof
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
omega
cof_eq_of_isNormal
isNormal_omega
cof_omega0 📖mathematicalcof
omega0
Cardinal.aleph0
LE.le.antisymm'
aleph0_le_cof
isSuccLimit_omega0
card_omega0
cof_le_card
cof_ord_le 📖mathematicalCardinal
Cardinal.instLE
cof
Cardinal.ord
Cardinal.card_ord
cof_le_card
cof_preOmega 📖mathematicalOrder.IsSuccPrelimit
Ordinal
Preorder.toLT
PartialOrder.toPreorder
partialOrder
cof
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
preOmega
IsMin.eq_bot
bot_eq_zero'
canonicallyOrderedAdd
preOmega_zero
cof_zero
cof_eq_of_isNormal
isNormal_preOmega
cof_succ 📖mathematicalcof
Order.succ
Ordinal
PartialOrder.toPreorder
partialOrder
instSuccOrder
Cardinal
Cardinal.instOne
le_antisymm
inductionOn
Sum.instIsWellOrderLex
instIsWellOrderEmptyRelationOfSubsingleton
Cardinal.mk_fintype
Fintype.card_unique
Nat.cast_one
cof_type_le
Set.mem_singleton
Cardinal.succ_zero
Order.succ_le_iff
Cardinal.instNoMaxOrder
Cardinal.canonicallyOrderedAdd
succ_ne_zero
cof_eq_zero
cof_type 📖mathematicalcof
type
Order.cof
Function.swap
Compl.compl
Pi.instCompl
Prop.instCompl
cof_type_le 📖mathematicalSet.UnboundedCardinal
Cardinal.instLE
cof
type
Set.Elem
le_cof_type
le_rfl
cof_type_lt 📖mathematicalcof
type
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Order.cof
Preorder.toLE
cof_type
compl_lt
Function.swap_ge
cof_univ 📖mathematicalcof
univ
Cardinal.univ
le_antisymm
cof_le_card
le_of_forall_lt
Cardinal.lt_univ'
isWellOrder_lt
wellFoundedLT
cof_eq
univ.eq_1
lift_cof
Cardinal.lift_lift
Cardinal.lift_lt
lt_of_not_ge
Cardinal.mem_range_lift_of_le
Order.lt_succ_iff
instNoMaxOrder
Equiv.apply_symm_apply
le_iSup
UnivLE.small
UnivLE.self
cof_zero 📖mathematicalcof
Ordinal
zero
Cardinal
Cardinal.instZero
LE.le.antisymm
card_zero
cof_le_card
Cardinal.zero_le
exists_blsub_cof 📖mathematicalblsub
Cardinal.ord
cof
exists_lsub_cof
Cardinal.ord_eq
blsub_eq_lsub'
exists_fundamental_sequence 📖mathematicalIsFundamentalSequence
Cardinal.ord
cof
exists_lsub_cof
Cardinal.ord_eq
RelEmbedding.isWellOrder
LE.le.trans
RelEmbedding.ordinal_type_le
le_refl
Subtype.prop
RelEmbedding.map_rel_iff'
enum_lt_enum
le_antisymm
blsub_le
lsub_le_iff
Eq.le
typein_lt_type
bfamilyOfFamily'_typein
IsWellFounded.wf
IsWellOrder.toIsWellFounded
Mathlib.Tactic.Push.not_forall_eq
WellFounded.min_mem
lt_of_lt_of_le
WellFounded.not_lt_min
IsTrans.trans
IsWellOrder.toIsTrans
LE.le.trans_lt
lt_blsub
LT.lt.trans_le
IsFundamentalSequence.ord_cof
exists_lsub_cof 📖mathematicallsub
cof
cof_eq_sInf_lsub
csInf_mem
Cardinal.instWellFoundedLT
cof_lsub_def_nonempty
iSup_lt 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Cardinal.ord
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
Cardinal.instConditionallyCompleteLinearOrderBot
iSup_lt_lift
Cardinal.lift_id
iSup_lt_lift 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
cof
Cardinal.ord
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
Cardinal.instConditionallyCompleteLinearOrderBot
Cardinal.ord_lt_ord
iSup_ord
iSup_lt_ord_lift
iSup_lt_ord 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Ordinal
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
iSup_lt_ord_lift
Cardinal.lift_id
iSup_lt_ord_lift 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
cof
Ordinal
partialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
instConditionallyCompleteLinearOrderBot
LE.le.trans_lt
iSup_le_lsub
lsub_lt_ord_lift
le_cof_iff_blsub 📖mathematicalCardinal
Cardinal.instLE
cof
card
le_cof_iff_lsub
Cardinal.mk_toType
type_toType
Cardinal.ord_eq
blsub_eq_lsub'
le_cof_iff_lsub 📖mathematicalCardinal
Cardinal.instLE
cof
cof_eq_sInf_lsub
le_csInf_iff''
cof_lsub_def_nonempty
le_cof_type 📖mathematicalCardinal
Cardinal.instLE
cof
type
Set.Elem
le_csInf_iff''
Std.Refl.swap
Std.Irrefl.compl
IsStrictOrder.toIrrefl
IsStrictTotalOrder.toIsStrictOrder
instIsStrictTotalOrderOfIsWellOrder
lift_cof 📖mathematicalCardinal.lift
cof
lift
inductionOn
RelIso.IsWellOrder.ulift
type_uLift
cof_type
Cardinal.lift_id'
Cardinal.lift_umax
RelIso.cof_eq_lift
Std.Refl.swap
Std.Irrefl.compl
Order.Preimage.instIrrefl
IsStrictOrder.toIrrefl
IsStrictTotalOrder.toIsStrictOrder
instIsStrictTotalOrderOfIsWellOrder
lsub_lt_ord 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
cof
Ordinal
partialOrder
lsublsub_lt_ord_lift
Cardinal.lift_id
lsub_lt_ord_lift 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.lift
cof
Ordinal
partialOrder
lsublt_of_le_of_ne
lsub_le
LE.le.not_gt
cof_lsub_le_lift
lt_cof_type 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Set.Elem
cof
type
Set.Boundednot_imp_not
cof_type_le
nfpFamily_lt_ord 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.aleph0
cof
Ordinal
partialOrder
nfpFamilynfpFamily_lt_ord_lift
Cardinal.lift_id
nfpFamily_lt_ord_lift 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.aleph0
cof
Cardinal.lift
Ordinal
partialOrder
nfpFamilyiSup_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 📖mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.aleph0
cof
Ordinal
partialOrder
nfpnfpFamily_lt_ord_lift
Cardinal.mk_fintype
Fintype.card_unique
Nat.cast_one
Cardinal.lift_one
LT.lt.trans
Cardinal.one_lt_aleph0
ord_cof_eq 📖mathematicalSet.Unbounded
type
Set
Set.instMembership
Subrel
Subrel.instIsWellOrderSubtype
Cardinal.ord
cof
Subrel.instIsWellOrderSubtype
cof_eq
Cardinal.ord_eq
IsWellFounded.wf
IsWellOrder.toIsWellFounded
WellFounded.min_mem
not_imp_not
WellFounded.not_lt_min
IsOrderConnected.neg_trans
isStrictOrderConnected_of_isStrictTotalOrder
instIsStrictTotalOrderOfIsWellOrder
le_antisymm
RelEmbedding.ordinal_type_le
Subrel.instTrichotomousSubtype
IsWellOrder.toTrichotomous
instAsymmOfIsWellFounded
trichotomous_of
asymm
Subrel.instAsymmSubtype
irrefl
Subrel.instIrreflSubtype
IsStrictOrder.toIrrefl
IsStrictTotalOrder.toIsStrictOrder
Cardinal.ord_le
cof_type_le
ord_cof_le 📖mathematicalOrdinal
Preorder.toLE
PartialOrder.toPreorder
partialOrder
Cardinal.ord
cof
LE.le.trans
Cardinal.ord_le_ord
cof_le_card
Cardinal.ord_card_le

Ordinal.IsFundamentalSequence

Theorems

NameKindAssumesProvesValidatesDepends On
blsub_eq 📖mathematicalOrdinal.IsFundamentalSequenceOrdinal.blsub
cof_eq 📖mathematicalOrdinal.IsFundamentalSequenceCardinal.ord
Ordinal.cof
LE.le.antisymm'
LE.le.trans
Cardinal.ord_le_ord
Ordinal.cof_blsub_le
Cardinal.ord_card_le
id_of_le_cof 📖mathematicalOrdinal
Preorder.toLE
PartialOrder.toPreorder
Ordinal.partialOrder
Cardinal.ord
Ordinal.cof
Ordinal.IsFundamentalSequenceOrdinal.blsub_id
lt 📖Ordinal.IsFundamentalSequence
Ordinal
Preorder.toLT
PartialOrder.toPreorder
Ordinal.partialOrder
Ordinal.lt_blsub
blsub_eq
monotone 📖Ordinal.IsFundamentalSequence
Ordinal
Preorder.toLT
PartialOrder.toPreorder
Ordinal.partialOrder
Preorder.toLE
lt_or_eq_of_le
LT.lt.le
le_refl
of_isNormal 📖Order.IsNormal
Ordinal
Ordinal.instLinearOrder
Order.IsSuccLimit
PartialOrder.toPreorder
Ordinal.partialOrder
Ordinal.IsFundamentalSequence
Ordinal.exists_lsub_cof
cof_eq
Cardinal.ord_le_ord
Ordinal.lt_lsub
Ordinal.lt_blsub_iff
Ordinal.IsNormal.blsub_eq
LE.le.antisymm
Ordinal.lsub_le
lt_of_le_of_lt
csInf_le'
le_of_forall_lt
Order.IsNormal.strictMono
Ordinal.lt_lsub_iff
LE.le.trans_lt
le_csInf_iff''
StrictMono.le_iff_le
LE.le.trans
Ordinal.cof_lsub_le
Ordinal.blsub_comp
StrictMono.monotone
ord_cof 📖mathematicalOrdinal.IsFundamentalSequenceCardinal.ord
Ordinal.cof
LT.lt.trans_le
Ordinal
PartialOrder.toPreorder
Ordinal.partialOrder
cof_eq
LT.lt.trans_le
strict_mono 📖Ordinal.IsFundamentalSequence
Ordinal
Preorder.toLT
PartialOrder.toPreorder
Ordinal.partialOrder
succ 📖mathematicalOrdinal.IsFundamentalSequence
Order.succ
Ordinal
PartialOrder.toPreorder
Ordinal.partialOrder
Ordinal.instSuccOrder
Ordinal.one
Ordinal.cof_succ
Cardinal.ord_one
le_refl
LT.lt.false
Ordinal.lt_one_iff_zero
Ordinal.blsub_const
Ordinal.one_ne_zero
trans 📖Ordinal.IsFundamentalSequencecof_eq
LE.le.trans
Ordinal.ord_cof_le
Ordinal.blsub_comp
monotone
zero 📖mathematicalOrdinal.IsFundamentalSequence
Ordinal
Ordinal.zero
Ordinal.cof_zero
Cardinal.ord_zero
le_refl
not_lt_zero
Ordinal.canonicallyOrderedAdd
Ordinal.blsub_zero

Ordinal.IsNormal

Theorems

NameKindAssumesProvesValidatesDepends On
cof_eq 📖mathematicalOrder.IsNormal
Ordinal
Ordinal.instLinearOrder
Order.IsSuccLimit
PartialOrder.toPreorder
Ordinal.partialOrder
Ordinal.cofOrdinal.cof_eq_of_isNormal
cof_le 📖mathematicalOrder.IsNormal
Ordinal
Ordinal.instLinearOrder
Cardinal
Cardinal.instLE
Ordinal.cof
Ordinal.cof_le_of_isNormal
isFundamentalSequence 📖Order.IsNormal
Ordinal
Ordinal.instLinearOrder
Order.IsSuccLimit
PartialOrder.toPreorder
Ordinal.partialOrder
Ordinal.IsFundamentalSequence
Ordinal.IsFundamentalSequence.of_isNormal

RelIso

Theorems

NameKindAssumesProvesValidatesDepends On
cof_eq 📖mathematicalOrder.cofcof_eq_lift
cof_eq_lift 📖mathematicalCardinal.lift
Order.cof
RelEmbedding.stdRefl
LE.le.antisymm

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