Theorems · Theorem
Function.Involutive.eq_iff
∀ {α : Sort u} {f : α → α}, Function.Involutive f → ∀ {x y : α}, f x = y ↔ x = f yAn involution commutes across an equality. Compare to Function.Injective.eq_iff.
- Defined in
- Mathlib.Logic.Function.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
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.
- Function.Involutivestatement and proof · cited by 103
- Function.Involutive.injectiveproof · cited by 26
Cited by22
Results whose statement or proof uses this declaration.
- neg_eq_iff_eq_negproof · cited by 60
- inv_eq_iff_eq_invproof · cited by 17
- PrimeSpectrum.iSup_basicOpen_eq_top_iffproof · cited by 6
- Matrix.transpose_eq_diagonalproof · cited by 4
- NumberField.InfinitePlace.card_filter_mk_eqproof · cited by 3
- Polynomial.mirror_eq_iffproof · cited by 2
- xor_eq_iff_left_eqproof · cited by 2
- ContextFreeGrammar.produces_reverseproof · cited by 1
- Matrix.map_star_eq_natCastproof · cited by 1
- Matrix.conjTranspose_eq_natCastproof · cited by 1
- xor_eq_iff_right_eqproof · cited by 1
- Finset.shadow_complsproof · cited by 0