Theorems · Theorem · group theory
Nat.card_perm
∀ {α : Type u_1} [Finite α], Nat.card (Equiv.Perm α) = (Nat.card α).factorial- Defined in
- Mathlib.Data.Finite.Perm
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Fintype.cardproof · cited by 1,386
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- Nat.factorialstatement and proof · cited by 616
- Fintype.ofFiniteproof · cited by 255
- Nat.card_eq_fintype_cardproof · cited by 200
- Fintype.card_permproof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- Equiv.Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_memproof · cited by 2
- Equiv.Perm.subgroup_eq_top_of_isPreprimitive_of_isSwap_memproof · cited by 1
- IsMultiplyPretransitive.alternatingGroup_leproof · cited by 1
- Equiv.Perm.has_swap_mem_of_lt_stabilizerproof · cited by 1
- Equiv.Perm.isCyclic_of_card_le_twoproof · cited by 1
- alternatingGroup.eq_bot_of_card_le_twoproof · cited by 1
- alternatingGroup.nontrivial_of_three_le_cardproof · cited by 1
- Equiv.Perm.subgroup_eq_top_of_nontrivialproof · cited by 0
- Equiv.Perm.isMultiplyPretransitive_of_nontrivialproof · cited by 0
- Subgroup.normal_of_index_eq_minFac_cardproof · cited by 0