Fixpoint findA (f : A -> bool) (l:list (A*B)) : option B :=
 match l with
  | nil => None
  | (a,b)::l => if f a then Some b else findA f l
 end.

(* Specifications: *)
Lemma findA_NoDupA : forall l a b, NoDupA (fun p p' => eqA (fst p) (fst p')) l -> (InA (fun p p' => eqA (fst p) (fst p') /\ snd p = snd p') (a,b) l <-> findA (fun a' => if eqA_dec a a' then true else false) l = Some b).