End Fold2.
Section Remove.
Hypothesis eqA_dec : forall x y : A, {eqA x y}+{~(eqA x y)}.

(* Specifications: *)
Lemma InA_dec : forall x l, { InA x l } + { ~ InA x l }.
Lemma removeA_InA : forall l x y, InA y (removeA x l) <-> InA y l /\ ~eqA x y.
Lemma removeA_NoDupA :
forall s x, NoDupA s ->  NoDupA (removeA x s).
Lemma removeA_equivlistA : forall l l' x,
~InA x l -> equivlistA (x :: l) l' -> equivlistA l (removeA x l').