Theorems · Theorem · group theory
Equiv.Perm.card_support_swap
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {x y : α}, x ≠ y → (Equiv.swap x y).support.card = 2- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement and proof · cited by 2,327
- Multiset.consproof · cited by 313
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.swapstatement and proof · cited by 197
- Finset.cons_eq_insertproof · cited by 59
- Multiset.nodup_consproof · cited by 10
- Equiv.Perm.support_swapproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.card_support_eq_twoproof · cited by 2
- alternatingGroup.isConj_swap_mul_swap_of_cycleType_twoproof · cited by 0