Documentation Verification Report

Jordan

📁 Source: Mathlib/GroupTheory/GroupAction/Jordan.lean

Statistics

MetricCount
Definitions0
TheoremsalternatingGroup_le_of_isPreprimitive_of_isThreeCycle_mem, eq_top_of_isPreprimitive_of_isSwap_mem, isMultiplyPretransitive_of_nontrivial, isPretransitive_of_isCycle_mem, subgroup_eq_top_of_isPreprimitive_of_isSwap_mem, subgroup_eq_top_of_nontrivial, isMultiplyPreprimitive, is_two_motive_of_is_motive, is_two_preprimitive, is_two_pretransitive, normalClosure_of_stabilizer_eq_top
11
Total11

Equiv.Perm

Theorems

NameKindAssumesProvesValidatesDepends On
alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_mem 📖mathematicalIsThreeCycle
Equiv.Perm
Subgroup
permGroup
SetLike.instMembership
Subgroup.instSetLike
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
alternatingGroup
alternatingGroup_le_of_index_le_two
Nat.card_pos
One.instNonempty
Subgroup.instFiniteSubtypeMem
Equiv.finite_left
Finite.of_fintype
Subgroup.index_mul_card
Nat.card_perm
le_trans
Nat.factorial_le
zero_add
mul_one
IsOrderedRing.toPosMulMono
IsStrictOrderedRing.toIsOrderedRing
Nat.instIsStrictOrderedRing
PosMulStrictMono.toPosMulReflectLE
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
IsThreeCycle.orderOf
Nat.card_eq_fintype_card
orderOf_dvd_card
IsMultiplyPretransitive.alternatingGroup_le
MulAction.IsPreprimitive.isMultiplyPreprimitive
Set.ncard_add_ncard_compl
Set.toFinite
Subtype.finite
Set.ncard_coe_finset
IsThreeCycle.card_support
add_comm
IsScalarTower.left
isPretransitive_of_isCycle_mem
IsThreeCycle.isCycle
MulAction.IsPreprimitive.of_prime_card
Fintype.card_subtype
Finset.ext
Finset.filter.congr_simp
Nat.prime_three
MulAction.IsMultiplyPreprimitive.isMultiplyPretransitive
eq_top_of_isPreprimitive_of_isSwap_mem 📖mathematicalIsSwap
Equiv.Perm
Subgroup
permGroup
SetLike.instMembership
Subgroup.instSetLike
Top.top
Subgroup.instTop
subgroup_eq_top_of_isPreprimitive_of_isSwap_mem
isMultiplyPretransitive_of_nontrivial 📖mathematicalNat.cardMulAction.IsMultiplyPretransitivefinite_or_infinite
Nat.card_eq_zero_of_infinite
Nat.instCharZero
Nat.instAtLeastTwoHAddOfNat
Function.bijective_id
MonoidHom.range_eq_top
Subgroup.eq_top_of_card_eq
Subgroup.instFiniteSubtypeMem
Equiv.finite_left
le_antisymm
Subgroup.card_le_card_group
Nat.card_perm
Set.eq_univ_of_univ_subset
map_one
MonoidHomClass.toOneHomClass
MonoidHom.instMonoidHomClass
one_smul
MulAction.IsPretransitive.of_embedding_congr
isMultiplyPretransitive
MulAction.isMultiplyPretransitive_of_le'
Nat.card_eq_fintype_card
ENat.card_eq_coe_fintype_card
not_nonempty_iff
Function.Embedding.nonempty_iff_card_le
Fintype.card_fin
MulAction.instIsPretransitiveOfSubsingleton
IsEmpty.instSubsingleton
isPretransitive_of_isCycle_mem 📖mathematicalIsCycle
Equiv.Perm
Subgroup
permGroup
SetLike.instMembership
Subgroup.instSetLike
MulAction.IsPretransitive
Subgroup.toGroup
fixingSubgroup
Subgroup.instMulAction
applyMulAction
Compl.compl
Set
Set.instCompl
SetLike.coe
Finset
Finset.instSetLike
support
SubMulAction
SemigroupAction.toSMul
Monoid.toSemigroup
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MulAction.toSemigroupAction
SubMulAction.instSetLike
SubMulAction.ofFixingSubgroup
SubMulAction.smul'
Monoid.toMulAction
IsScalarTower.left
IsScalarTower.left
mem_fixingSubgroup_iff
MulAction.isPretransitive_iff
SetLike.coe_eq_coe
smul_smul
inv_mul_cancel_right
subgroup_eq_top_of_isPreprimitive_of_isSwap_mem 📖mathematicalIsSwap
Equiv.Perm
Subgroup
permGroup
SetLike.instMembership
Subgroup.instSetLike
Top.top
Subgroup.instTop
Subgroup.eq_top_of_card_eq
Subgroup.instFiniteSubtypeMem
Equiv.finite_left
Nat.card_eq_fintype_card
le_antisymm
Fintype.card_subtype_le
Nat.card_perm
le_trans
Nat.factorial_le
Nat.factorial_two
One.instNonempty
Fintype.card_pos
IsSwap.orderOf
orderOf_submonoid
orderOf_dvd_card
Set.ncard_add_ncard_compl
Set.toFinite
Subtype.finite
Set.ncard_coe_finset
card_support_eq_two
add_comm
eq_top_of_isMultiplyPretransitive
MulAction.IsPreprimitive.isMultiplyPreprimitive
IsScalarTower.left
isPretransitive_of_isCycle_mem
IsSwap.isCycle
MulAction.IsPreprimitive.of_prime_card
Fintype.card_subtype
Finset.filter.congr_simp
Finset.coe_filter
Nat.prime_two
MulAction.IsMultiplyPreprimitive.isMultiplyPretransitive
subgroup_eq_top_of_nontrivial 📖mathematicalNat.cardTop.top
Subgroup
Equiv.Perm
permGroup
Subgroup.instTop
Subgroup.eq_top_of_le_card
Equiv.finite_left
Nat.card_perm
LE.le.trans
Nat.factorial_le
Nat.factorial_two
Subgroup.one_lt_card_iff_ne_bot
Subgroup.instFiniteSubtypeMem
Subgroup.nontrivial_iff_ne_bot

MulAction.IsPreprimitive

Theorems

NameKindAssumesProvesValidatesDepends On
isMultiplyPreprimitive 📖mathematicalSet.ncard
Nat.card
MulAction.IsMultiplyPreprimitiveIsScalarTower.left
finite_or_infinite
Nat.card_eq_zero_of_infinite
Nat.instCanonicallyOrderedAdd
zero_add
is_two_preprimitive
Set.ncard_pos
Set.toFinite
Subtype.finite
Set.ext
Set.mem_image
Subtype.prop
Set.mem_singleton
MulAction.is_one_preprimitive_iff
MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizer
MulAction.IsQuasiPreprimitive.toIsPretransitive
isQuasiPreprimitive
Mathlib.Meta.NormNum.isNat_le_true
IsStrictOrderedRing.toIsOrderedRing
Nat.instIsStrictOrderedRing
Mathlib.Meta.NormNum.isNat_ofNat
of_surjective
Function.Bijective.surjective
SubMulAction.ofFixingSubgroup_of_eq_bijective
Subgroup.instIsScalarTowerSubtypeMem
SubMulAction.isScalarTower'
SubMulAction.ofFixingSubgroup_insert_map_bijective
Set.ncard_image_of_injective
Subtype.val_injective
Set.ncard_insert_of_notMem
Finite.Set.finite_image
SubMulAction.nat_card_ofStabilizer_add_one_eq
is_two_motive_of_is_motive 📖mathematicalSet.ncard
Nat.card
MulAction.IsMultiplyPretransitive
MulAction.IsMultiplyPreprimitive
Nat.strong_induction_on
IsScalarTower.left
Nat.finite_of_card_ne_zero
ne_zero_of_lt
Set.ncard_univ
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
contravariant_lt_of_covariant_le
Nat.instZeroLEOneClass
Nat.instCharZero
Nat.instAtLeastTwoHAddOfNat
Set.ncard_pos
Set.toFinite
Subtype.finite
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
contravariant_swap_add_of_contravariant_add
Nat.instNoMaxOrder
Nat.instCanonicallyOrderedAdd
zero_add
SubMulAction.ofStabilizer.isMultiplyPretransitive
MulAction.IsQuasiPreprimitive.toIsPretransitive
isQuasiPreprimitive
MulAction.is_one_pretransitive_iff
MulAction.IsPretransitive.of_surjective_map
mem_fixingSubgroup_iff
Set.mem_singleton
Function.Bijective.surjective
SubMulAction.ofFixingSubgroup_of_singleton_bijective
MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizer
le_rfl
MulAction.is_one_preprimitive_iff
of_surjective
Set.one_lt_ncard
exists_mem_smul_and_notMem_smul
Set.Finite.inter_of_left
Set.ncard_ne_zero_of_mem
Set.ncard_lt_ncard
Set.inter_subset_left
Set.inter_subset_right
lt_trans
SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_inter
Set.union_ne_univ_of_ncard_add_ncard_lt
Set.ncard_smul_set
two_mul
SubMulAction.IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter
Set.one_lt_encard_iff_nontrivial
Set.Finite.cast_ncard_eq
Nat.one_lt_cast
IsOrderedRing.toIsOrderedAddMonoid
IsOrderedRing.toZeroLEOneClass
Set.ncard_add_ncard_compl
add_comm
Set.nonempty_of_mem
Set.smul_set_compl
Finite.Set.finite_inter_of_left
Set.nonempty_inter_of_le_ncard_add_ncard
Set.eq_of_subset_of_ncard_le
subset_trans
Set.instIsTransSubset
le_refl
Set.mem_univ
is_two_preprimitive 📖mathematicalSet.ncard
Nat.card
MulAction.IsMultiplyPreprimitiveIsScalarTower.left
is_two_motive_of_is_motive
is_two_pretransitive 📖mathematicalSet.ncard
Nat.card
MulAction.IsMultiplyPretransitiveIsScalarTower.left
is_two_motive_of_is_motive

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
normalClosure_of_stabilizer_eq_top 📖mathematicalENat
Preorder.toLT
PartialOrder.toPreorder
OmegaCompletePartialOrder.toPartialOrder
CompleteLattice.instOmegaCompletePartialOrder
CompletelyDistribLattice.toCompleteLattice
CompleteLinearOrder.toCompletelyDistribLattice
instCompleteLinearOrderENat
instOfNatAtLeastTwo
ENat.instNatCast
Nat.instAtLeastTwoHAddOfNat
ENat.card
Subgroup.normalClosure
SetLike.coe
Subgroup
Subgroup.instSetLike
MulAction.stabilizer
Top.top
Subgroup.instTop
Nat.instAtLeastTwoHAddOfNat
MulAction.is_one_pretransitive_iff
MulAction.isMultiplyPretransitive_of_le'
one_le_two
Nat.instZeroLEOneClass
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
le_of_lt
ENat.one_lt_card_iff_nontrivial
lt_trans
Mathlib.Meta.NormNum.isNat_lt_true
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
Mathlib.Meta.NormNum.instAtLeastTwo
MulAction.isCoatom_stabilizer_iff_preprimitive
MulAction.isPreprimitive_of_is_two_pretransitive
Subgroup.le_normalClosure
lt_of_add_lt_add_right
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
IsOrderedRing.toIsOrderedAddMonoid
SubMulAction.ENat_card_ofStabilizer_add_one_eq
nontrivial_iff
IsScalarTower.left
SubMulAction.ofStabilizer.isMultiplyPretransitive
MulAction.exists_smul_eq
SetLike.coe_eq_coe
SubMulAction.instSMulMemClass
SetLike.val_smul
inv_smul_eq_iff
smul_smul
Subgroup.Normal.conj_mem
Subgroup.normalClosure_normal

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