(** [map] and count of occurrences *)
Hypothesis decA: forall x1 x2 : A, {x1 = x2} + {x1 <> x2}.
Hypothesis decB: forall y1 y2 : B, {y1 = y2} + {y1 <> y2}.
Hypothesis Hfinjective: forall x1 x2: A, (f x1) = (f x2) -> x1 = x2.

Theorem count_occ_map x l:
count_occ decA l x = count_occ decB (map l) (f x).