Section ForallNorm.
Variable T : Type.
Variable P : T -> Prop.
(* use: rewrite ?Forall_norm *)
Definition Forall_norm := (@Forall_appP, @Forall_singletonP, @Forall_consP, @Forall_nilP).
End ForallNorm.

Lemma count_occ_cons {X : Type} {D : forall x y : X, {x = y} + {x <> y}} {A a c}:
count_occ D (a :: A) c = count_occ D (locked [a]) c + count_occ D A c.