Theorems · Theorem
Equiv.swap_apply_of_ne_of_ne
∀ {α : Sort u_1} [inst : DecidableEq α] {a b x : α}, x ≠ a → x ≠ b → (Equiv.swap a b) x = x- Defined in
- Mathlib.Logic.Equiv.Basic
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 18 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equiv.Permstatement · cited by 1,375
- Equiv.swapstatement · cited by 197
Cited by39
Results whose statement or proof uses this declaration.
- MonovaryOn.sum_smul_comp_perm_le_sum_smulproof · cited by 7
- MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iffproof · cited by 5
- alternatingGroup.isMultiplyPretransitiveproof · cited by 4
- Equiv.swap_mul_swap_mul_swapproof · cited by 4
- Similar.comm_leftproof · cited by 3
- Equiv.Perm.card_support_eq_twoproof · cited by 2
- alternatingGroup.center_eq_botproof · cited by 2
- Matrix.cons_cons_comp_swap_zero_oneproof · cited by 2
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2
- Similar.comm_rightproof · cited by 2
- Pi.lex_descproof · cited by 2
- Equiv.Perm.swap_mem_stabilizerproof · cited by 2