Section Permutation_map.
Variable A B : Type.
Variable f : A -> B.
Global Instance Permutation_map' :
Proper (@Permutation A ==> @Permutation B) (map f) | 10.
End Permutation_map.

Lemma nat_bijection_Permutation n f :
bFun n f ->
Injective f ->
let l := seq 0 n in Permutation (map f l) l.