Theorems · Definition · group theory
Equiv.Perm.IsSwap
{α : Type u_1} → [DecidableEq α] → Equiv.Perm α → Propf.IsSwap indicates that the permutation f is a transposition of two elements.
- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.swapproof · cited by 197
Cited by38
Results whose statement or proof uses this declaration.
- Equiv.Perm.truncSwapFactorsstatement · cited by 5
- Equiv.Perm.swap_induction_onproof · cited by 5
- Equiv.Perm.IsSwap.isCyclestatement and proof · cited by 4
- Equiv.Perm.sign_prod_list_swapstatement and proof · cited by 3
- Equiv.Perm.closure_isSwapstatement · cited by 3
- Equiv.Perm.closure_three_cycles_eq_alternatingproof · cited by 3
- Equiv.Perm.IsSwap.sign_eqstatement and proof · cited by 3
- Equiv.Perm.swap_isSwap_iffstatement and proof · cited by 3
- surjective_of_isSwap_of_isPretransitive'statement and proof · cited by 2
- mem_closure_isSwapstatement and proof · cited by 2
- Equiv.Perm.card_support_eq_twostatement and proof · cited by 2
- alternatingGroup.stabilizer.surjective_toPermproof · cited by 2