Theorems · Theorem
Function.Involutive.bijective
∀ {α : Sort u} {f : α → α}, Function.Involutive f → Function.Bijective f- Defined in
- Mathlib.Logic.Function.Basic
- Cited by
- 21 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.Bijectivestatement · cited by 863
- Function.Involutivestatement and proof · cited by 103
- Function.Involutive.injectiveproof · cited by 26
- Function.Involutive.surjectiveproof · cited by 23
Cited by21
Results whose statement or proof uses this declaration.
- Matrix.det_transposeproof · cited by 51
- ContextFreeRule.reverse_bijectiveproof · cited by 4
- ContextFreeGrammar.reverse_bijectiveproof · cited by 2
- Matrix.permanent_transposeproof · cited by 2
- compl_bijectiveproof · cited by 1
- unitInterval.symm_bijectiveproof · cited by 1
- List.foldl_range_subset_of_range_subsetproof · cited by 1
- inv_bijectiveproof · cited by 0
- List.reverse_bijectiveproof · cited by 0
- neg_bijectiveproof · cited by 0
- RootPairing.GeckConstruction.ωConjLieSubmodule_eq_top_iffproof · cited by 0
- Language.reverse_bijectiveproof · cited by 0