Section SurjectInject.
Variable (sig tau : Type).
Variable def : sig.
Variable retr : Retract sig tau.
Definition injectSymbols : list sig -> list tau := map Retr_f.
Definition surjectSymbols : list tau -> list sig := map (surject Retr_g def).
End SurjectInject.

Corollary map_length_eq : forall (A B C : Type) (f : A -> C) (g : B -> C) (l1 : list A) (l2 : list B), map f l1 = map g l2 -> |l1| = |l2|.