proposition: Theorem nth_option_app_Some : forall (A : Set)(ls1 ls2 : list A) i a, nth_option ls1 i = Some a -> nth_option (ls1 ++ ls2) i = Some a.
proof: Proof. induction ls1; intuition; simpl in *. congruence. destruct i; trivial. eauto. Qed.
imports: FCF.Rat List Permutation Arith FCF.EqDec FCF.StdNat Bool Permutation