Theorems · Theorem · group theory
Equiv.Perm.support_swap
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {x y : α}, x ≠ y → (Equiv.swap x y).support = {x, y}- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 57 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Perm.supportstatement · cited by 230
- Equiv.swapstatement · cited by 197
Cited by8
Results whose statement or proof uses this declaration.
- Equiv.Perm.isThreeCycle_swap_mul_swap_sameproof · cited by 2
- alternatingGroup.stabilizer.surjective_toPermproof · cited by 2
- Equiv.Perm.card_support_swapproof · cited by 2
- alternatingGroup.isConj_ofproof · cited by 1
- Equiv.Perm.count_le_one_of_centralizer_le_alternatingproof · cited by 1
- alternatingGroup.isConj_swap_mul_swap_of_cycleType_twoproof · cited by 0
- Equiv.Perm.support_swap_iffproof · cited by 0
- Equiv.Perm.support_swap_mul_swapproof · cited by 0