Theorems · Theorem · group theory
Equiv.Perm.card_support_eq_two
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {f : Equiv.Perm α}, f.support.card = 2 ↔ f.IsSwap- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement and proof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.swapproof · cited by 197
- Finset.mem_singletonproof · cited by 103
- Equiv.Perm.extproof · cited by 75
- Equiv.Perm.mem_supportproof · cited by 51
- Finset.mem_insertproof · cited by 44
- Equiv.swap_apply_leftproof · cited by 44
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.subgroup_eq_top_of_isPreprimitive_of_isSwap_memproof · cited by 1
- Polynomial.Gal.galActionHom_bijective_of_prime_degreeproof · cited by 1