Theorems · Theorem
Equiv.swap_self
∀ {α : Sort u_1} [inst : DecidableEq α] (a : α), Equiv.swap a a = Equiv.refl α- Defined in
- Mathlib.Logic.Equiv.Basic
- Cited by
- 18 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.
Cites5
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.reflstatement · cited by 274
- Equiv.swapstatement · cited by 197
- Equiv.extproof · cited by 102
- Equiv.swapCore_selfproof · cited by 1
Cited by18
Results whose statement or proof uses this declaration.
- Equiv.Perm.sign_swap'proof · cited by 10
- MonovaryOn.sum_smul_comp_perm_le_sum_smulproof · cited by 7
- Equiv.Perm.decomposeFin_symm_apply_succproof · cited by 3
- Equiv.Perm.swap_isSwap_iffproof · cited by 3
- Equiv.Perm.decomposeFin.symm_signproof · cited by 2
- Equiv.bijOn_swapproof · cited by 1
- finRotate_succ_eq_decomposeFinproof · cited by 1
- Matrix.adjp_none_noneproof · cited by 1
- Equiv.Perm.IsThreeCycle.eq_swap_mul_swap_iff_mem_supportproof · cited by 1
- swap_mem_closure_isSwapproof · cited by 1
- Equiv.Perm.closure_cycle_adjacent_swapproof · cited by 1
- SubmonoidClass.swap_mem_transproof · cited by 1