proposition: Lemma lookup_funTable x d: lookup x funTable d = f x.
proof: Proof. unfold funTable. specialize (elem_spec x). generalize (elem X) as l. induction l;cbn;intros Hel. - tauto. - destruct (eqb_spec x a). + congruence. + destruct Hel. 1:congruence. eauto. Qed.
imports: Undecidability.L.Tactics(LTactics) Undecidability.L.Datatypes(LFinType LBool LProd) Undecidability.L.Functions(EqBool)