Theorems · Definition
Equiv.swap
{α : Sort u_1} → [DecidableEq α] → α → α → Equiv.Perm αswap a b is the permutation that swaps a and b and
leaves other values as is.
- Defined in
- Mathlib.Logic.Equiv.Basic
- Cited by
- 197 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 91 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.Permstatement · cited by 1,375
- Equiv.swapCoreproof · cited by 3
- Equiv.swapCore_swapCoreproof · cited by 1
Cited by204
Results whose statement or proof uses this declaration.
- List.formPermproof · cited by 54
- Equiv.swap_apply_leftstatement · cited by 44
- Equiv.swap_apply_of_ne_of_nestatement · cited by 39
- Equiv.Perm.IsSwapproof · cited by 35
- Equiv.swap_apply_rightstatement · cited by 31
- Matrix.swapproof · cited by 19
- Equiv.swap_selfstatement · cited by 18
- Equiv.swap_commstatement · cited by 11
- Equiv.Perm.sign_swapstatement · cited by 10
- Equiv.Perm.sign_swap'statement and proof · cited by 10
- Equiv.Perm.decomposeOptionproof · cited by 10
- Equiv.Perm.support_swapstatement · cited by 8
Showing the 200 most cited of 204.