unfold funcCollision.
intuition.
simpl in *.
destruct (findCollision_1 eqda eqdb ls a0 b0).
trivial.
trivial.
Qed.

Theorem F_randomFunc_preserves_coll :
forall c0 x d a b0,
funcCollision _ _ (fst (split c0)) = true ->
In (a, b0) (getSupport (F_randomFunc x c0 d)) ->
funcCollision _ _ (fst (split b0)) = true.