proposition: Lemma nth_error_set_nth_none m n a b : nth_error st m = None -> nth_error st n = Some a -> nth_error (set_nth def st n b) m = None.
proof: Proof. by elim: m st n => [|m IH] [|c st'] [|n] //=; apply IH. Qed.
imports: mathcomp(all_ssreflect)