Documentation Verification Report

JordanHolder

📁 Source: Mathlib/Order/JordanHolder.lean

Statistics

MetricCount
DefinitionsCompositionSeries, Equivalent, JordanHolderLattice, IsMaximal
4
Theoremslength_eq, refl, smash, snoc, snoc_snoc_swap, trans, eq_of_head_eq_head_of_last_eq_last_of_length_eq_zero, eq_snoc_eraseLast, exists_last_eq_snoc_equivalent, ext, ext_iff, head_le, head_le_of_mem, inj, injective, isMaximal_eraseLast_last, jordan_holder, last_eraseLast_le, le_last, le_last_of_mem, length_eq_zero_of_head_eq_head_of_last_eq_last_of_length_eq_zero, length_pos_of_head_eq_head_of_last_eq_last_of_length_pos, lt_last_of_mem_eraseLast, lt_succ, mem_eraseLast, mem_eraseLast_of_ne_of_mem, snoc_eraseLast_last, strictMono, toList_nodup, toList_sorted, total, iso_refl, isMaximal_inf_left_of_isMaximal_sup, isMaximal_inf_right_of_isMaximal_sup, isMaximal_of_eq_inf, iso_symm, iso_trans, lt_of_isMaximal, second_iso, second_iso_of_eq, sup_eq_of_isMaximal
41
Total45

CompositionSeries

Definitions

NameCategoryTheorems
Equivalent 📖MathDef
4 mathmath: jordan_holder, Equivalent.snoc_snoc_swap, exists_last_eq_snoc_equivalent, Equivalent.refl

Theorems

NameKindAssumesProvesValidatesDepends On
eq_of_head_eq_head_of_last_eq_last_of_length_eq_zero 📖RelSeries.head
setOf
JordanHolderLattice.IsMaximal
RelSeries.last
RelSeries.length
RelSeries.subsingleton_of_length_eq_zero
RelSeries.last_mem
length_eq_zero_of_head_eq_head_of_last_eq_last_of_length_eq_zero
ext
eq_snoc_eraseLast 📖mathematicalRelSeries.length
setOf
JordanHolderLattice.IsMaximal
RelSeries.snoc
RelSeries.eraseLast
RelSeries.last
isMaximal_eraseLast_last
ext
isMaximal_eraseLast_last
mem_eraseLast
RelSeries.last_mem
exists_last_eq_snoc_equivalent 📖mathematicalJordanHolderLattice.IsMaximal
RelSeries.last
setOf
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.head
RelSeries.length
Equivalent
RelSeries.snoc
ne_of_gt
lt_of_le_of_lt
JordanHolderLattice.lt_of_isMaximal
RelSeries.subsingleton_of_length_eq_zero
RelSeries.last_mem
RelSeries.head_mem
add_tsub_cancel_right
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
snoc_eraseLast_last
JordanHolderLattice.isMaximal_of_eq_inf
isMaximal_eraseLast_last
le_inf
le_last_of_mem
inf_comm
RelSeries.head_snoc
RelSeries.last_snoc
eq_snoc_eraseLast
Equivalent.snoc
JordanHolderLattice.IsMaximal.iso_refl
Equivalent.trans
Equivalent.snoc_snoc_swap
JordanHolderLattice.iso_symm
JordanHolderLattice.second_iso_of_eq
JordanHolderLattice.sup_eq_of_isMaximal
ext 📖CompositionSeries
RelSeries.membership
setOf
JordanHolderLattice.IsMaximal
RelSeries.toList_injective
List.Perm.eq_of_pairwise'
instAntisymmLt
List.SortedLT.pairwise
toList_sorted
List.perm_of_nodup_nodup_toFinset_eq
toList_nodup
ext_iff 📖mathematicalCompositionSeries
RelSeries.membership
setOf
JordanHolderLattice.IsMaximal
ext
head_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.head
setOf
JordanHolderLattice.IsMaximal
RelSeries.toFun
StrictMono.monotone
strictMono
head_le_of_mem 📖mathematicalCompositionSeries
RelSeries.membership
setOf
JordanHolderLattice.IsMaximal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.head
Set.mem_range
head_le
inj 📖mathematicalRelSeries.toFun
setOf
JordanHolderLattice.IsMaximal
injective
injective 📖mathematicalRelSeries.length
setOf
JordanHolderLattice.IsMaximal
RelSeries.toFun
StrictMono.injective
strictMono
isMaximal_eraseLast_last 📖mathematicalRelSeries.length
setOf
JordanHolderLattice.IsMaximal
RelSeries.last
RelSeries.eraseLast
RelSeries.last_eraseLast
RelSeries.last.eq_1
RelSeries.step
tsub_add_cancel_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
Nat.instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
Nat.instOrderedSub
jordan_holder 📖mathematicalRelSeries.head
setOf
JordanHolderLattice.IsMaximal
RelSeries.last
Equivalenteq_of_head_eq_head_of_last_eq_last_of_length_eq_zero
Equivalent.refl
length_pos_of_head_eq_head_of_last_eq_last_of_length_pos
isMaximal_eraseLast_last
exists_last_eq_snoc_equivalent
head_le_of_mem
RelSeries.last_mem
RelSeries.head_eraseLast
Equivalent.trans
eq_snoc_eraseLast
RelSeries.snoc.congr_simp
Equivalent.snoc
JordanHolderLattice.IsMaximal.iso_refl
last_eraseLast_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.last
setOf
JordanHolderLattice.IsMaximal
RelSeries.eraseLast
StrictMono.le_iff_le
strictMono
Nat.instOrderedSub
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
Nat.instCanonicallyOrderedAdd
le_last 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.toFun
setOf
JordanHolderLattice.IsMaximal
RelSeries.last
StrictMono.monotone
strictMono
le_last_of_mem 📖mathematicalCompositionSeries
RelSeries.membership
setOf
JordanHolderLattice.IsMaximal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.last
Set.mem_range
le_last
length_eq_zero_of_head_eq_head_of_last_eq_last_of_length_eq_zero 📖RelSeries.head
setOf
JordanHolderLattice.IsMaximal
RelSeries.last
RelSeries.length
injective
zero_add
length_pos_of_head_eq_head_of_last_eq_last_of_length_pos 📖RelSeries.head
setOf
JordanHolderLattice.IsMaximal
RelSeries.last
RelSeries.length
not_imp_not
Nat.instCanonicallyOrderedAdd
length_eq_zero_of_head_eq_head_of_last_eq_last_of_length_eq_zero
lt_last_of_mem_eraseLast 📖mathematicalRelSeries.length
setOf
JordanHolderLattice.IsMaximal
RelSeries
RelSeries.membership
RelSeries.eraseLast
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.last
lt_of_le_of_ne
le_last_of_mem
mem_eraseLast
lt_succ 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.toFun
setOf
JordanHolderLattice.IsMaximal
RelSeries.length
JordanHolderLattice.lt_of_isMaximal
RelSeries.step
mem_eraseLast 📖mathematicalRelSeries.length
setOf
JordanHolderLattice.IsMaximal
RelSeries
RelSeries.membership
RelSeries.eraseLast
CompositionSeries
ne_of_lt
mem_eraseLast_of_ne_of_mem
mem_eraseLast_of_ne_of_mem 📖mathematicalCompositionSeries
RelSeries.membership
setOf
JordanHolderLattice.IsMaximal
RelSeries
RelSeries.eraseLast
RelSeries.length_pos_of_nontrivial
RelSeries.last_mem
lt_of_le_of_ne
snoc_eraseLast_last 📖mathematicalJordanHolderLattice.IsMaximal
RelSeries.last
setOf
RelSeries.eraseLast
RelSeries.snocne_of_gt
JordanHolderLattice.lt_of_isMaximal
Nat.instCanonicallyOrderedAdd
zero_add
isMaximal_eraseLast_last
eq_snoc_eraseLast
strictMono 📖mathematicalStrictMono
RelSeries.length
setOf
JordanHolderLattice.IsMaximal
PartialOrder.toPreorder
Fin.instPartialOrder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.toFun
Fin.strictMono_iff_lt_succ
lt_succ
toList_nodup 📖mathematicalRelSeries.toList
setOf
JordanHolderLattice.IsMaximal
List.SortedLT.nodup
toList_sorted
toList_sorted 📖mathematicalList.SortedLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
RelSeries.toList
setOf
JordanHolderLattice.IsMaximal
List.IsChain.sortedLT
RelSeries.toList_getElem
strictMono
total 📖mathematicalCompositionSeries
RelSeries.membership
setOf
JordanHolderLattice.IsMaximal
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Set.mem_range
StrictMono.le_iff_le
strictMono
le_total

CompositionSeries.Equivalent

Theorems

NameKindAssumesProvesValidatesDepends On
length_eq 📖mathematicalCompositionSeries.EquivalentRelSeries.length
setOf
JordanHolderLattice.IsMaximal
Fintype.card_fin
Fintype.card_congr
refl 📖mathematicalCompositionSeries.EquivalentJordanHolderLattice.IsMaximal.iso_refl
RelSeries.step
smash 📖mathematicalRelSeries.last
setOf
JordanHolderLattice.IsMaximal
RelSeries.head
CompositionSeries.Equivalent
RelSeries.smashRelSeries.smash_castAdd
RelSeries.smash_succ_castAdd
finSumFinEquiv_symm_apply_castAdd
RelSeries.smash_natAdd
RelSeries.smash_succ_natAdd
finSumFinEquiv_symm_apply_natAdd
snoc 📖mathematicalJordanHolderLattice.IsMaximal
RelSeries.last
setOf
CompositionSeries.Equivalent
JordanHolderLattice.Iso
RelSeries.snocRelSeries.snoc_castSucc
RelSeries.last_snoc'
finSuccEquivLast_last
finSuccEquivLast_symm_none
finSuccEquivLast_castSucc
finSuccEquivLast_symm_some
snoc_snoc_swap 📖mathematicalJordanHolderLattice.IsMaximal
RelSeries.last
setOf
RelSeries.snoc
JordanHolderLattice.Iso
CompositionSeries.EquivalentEquiv.swap_apply_left
RelSeries.snoc_castSucc
RelSeries.last_snoc
Equiv.swap_apply_right
RelSeries.last_snoc'
Equiv.swap_apply_of_ne_of_ne
JordanHolderLattice.IsMaximal.iso_refl
RelSeries.step
trans 📖CompositionSeries.EquivalentJordanHolderLattice.iso_trans

JordanHolderLattice

Definitions

NameCategoryTheorems
IsMaximal 📖MathDef
13 mathmath: CompositionSeries.le_last, CompositionSeries.last_eraseLast_le, isFiniteLength_iff_exists_compositionSeries, CompositionSeries.lt_succ, exists_compositionSeries_of_isNoetherian_isArtinian, CompositionSeries.Equivalent.length_eq, CompositionSeries.strictMono, CompositionSeries.ext_iff, CompositionSeries.injective, CompositionSeries.toList_sorted, CompositionSeries.toList_nodup, CompositionSeries.inj, CompositionSeries.head_le

Theorems

NameKindAssumesProvesValidatesDepends On
isMaximal_inf_left_of_isMaximal_sup 📖mathematicalIsMaximal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
Lattice.toSemilatticeInf
isMaximal_inf_right_of_isMaximal_sup 📖mathematicalIsMaximal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
Lattice.toSemilatticeInf
inf_comm
isMaximal_inf_left_of_isMaximal_sup
sup_comm
isMaximal_of_eq_inf 📖SemilatticeInf.toMin
Lattice.toSemilatticeInf
IsMaximal
sup_eq_of_isMaximal
isMaximal_inf_right_of_isMaximal_sup
iso_symm 📖Iso
iso_trans 📖Iso
lt_of_isMaximal 📖mathematicalIsMaximalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
second_iso 📖mathematicalIsMaximal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Iso
SemilatticeInf.toMin
Lattice.toSemilatticeInf
second_iso_of_eq 📖mathematicalIsMaximal
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
Lattice.toSemilatticeInf
Isosecond_iso
sup_eq_of_isMaximal 📖mathematicalIsMaximalSemilatticeSup.toMax
Lattice.toSemilatticeSup

JordanHolderLattice.IsMaximal

Theorems

NameKindAssumesProvesValidatesDepends On
iso_refl 📖mathematicalJordanHolderLattice.IsMaximalJordanHolderLattice.IsoJordanHolderLattice.second_iso_of_eq
sup_eq_right
le_of_lt
JordanHolderLattice.lt_of_isMaximal
inf_eq_left

(root)

Definitions

NameCategoryTheorems
CompositionSeries 📖CompOp
2 mathmath: CompositionSeries.ext_iff, CompositionSeries.mem_eraseLast
JordanHolderLattice 📖CompData

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