intuition.
destruct (eqda a1 a2).
subst.
right.
intuition.
subst.
intuition.
left.
intuition.
Qed.

(* Specifications: *)
Theorem map_ne_same_ex :
forall (A B : Set)(f1 f2 : A -> B)(ls : list A),
eq_dec B ->
map f1 ls <> map f2 ls ->
exists a, In a ls /\ f1 a <> f2 a.