proposition: Theorem firstn_app_le : forall (A : Type)(n : nat)(ls1 ls2 : list A), (n <= length ls1)%nat -> firstn n (ls1 ++ ls2) = firstn n ls1.
proof: Proof. induction n; destruct ls1; intuition idtac; simpl in *. lia. f_equal. eapply IHn. lia. Qed.
imports: FCF.Rat List Permutation Arith FCF.EqDec FCF.StdNat Bool Permutation