Theorems · Theorem · group theory
Equiv.Perm.isMulCommutative_iff_card_le_two
∀ {α : Type u_1} [Finite α], IsMulCommutative (Equiv.Perm α) ↔ Nat.card α ≤ 2- Defined in
- Mathlib.Data.Finite.Perm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.univproof · cited by 3,945
- Finitestatement and proof · cited by 3,029
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- not_ltproof · cited by 306
- Equiv.swapproof · cited by 197
- Set.toFiniteproof · cited by 174
- IsMulCommutativestatement and proof · cited by 95
- Equiv.swap_apply_leftproof · cited by 44
- Equiv.swap_apply_of_ne_of_neproof · cited by 39
- Set.ncard_univproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.isCyclic_iff_card_le_twoproof · cited by 0