proposition: Theorem nth_combine : forall (A B : Type)(lsA : list A)(lsB : list B) n defA defB, length lsA = length lsB -> nth n (combine lsA lsB) (defA, defB) = (nth n lsA defA, nth n lsB defB).
proof: Proof. induction lsA; destruct lsB; destruct n; intuition idtac; simpl in *; try lia. eapply IHlsA. lia. Qed.
imports: FCF.Rat List Permutation Arith FCF.EqDec FCF.StdNat Bool Permutation