proposition: Lemma nth_error_sapp X L (x: X) n sigma: nth_error L n = Some x -> (L .+ sigma) n = x.
proof: Proof. induction L in n |-*; cbn. + destruct n; cbn in *; discriminate. + firstorder. destruct n; cbn in *. congruence. eauto. Qed.
imports: List Arith Lia Morphisms Undecidability.HOU(calculus.terms)