Theorems · Theorem
Equiv.swap_comm
∀ {α : Sort u_1} [inst : DecidableEq α] (a b : α), Equiv.swap a b = Equiv.swap b a- Defined in
- Mathlib.Logic.Equiv.Basic
- Cited by
- 11 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.
Cites4
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.swapstatement · cited by 197
- Equiv.extproof · cited by 102
- Equiv.swapCore_commproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- Equiv.swap_mul_swap_mul_swapproof · cited by 4
- Equiv.Perm.isConj_swapproof · cited by 3
- Matrix.swap_commproof · cited by 2
- swap_mem_closure_isSwapproof · cited by 1
- Equiv.Perm.closure_cycle_adjacent_swapproof · cited by 1
- Equiv.Perm.isCycle_swap_mul_aux₂proof · cited by 1
- SubmonoidClass.swap_mem_transproof · cited by 1
- Equiv.swap_injective_of_rightproof · cited by 0
- Equiv.Perm.mclosure_swap_castSucc_succproof · cited by 0
- Equiv.Perm.IsSwap.mul_mem_closure_three_cyclesproof · cited by 0
- Pi.colex_ascproof · cited by 0