proposition: Lemma multi_step_repeat_solI n : multi_step srs (repeat sz n ++ [so]) (repeat so (n+1)).
proof: Proof. elim: n; first by apply: rt_refl. move=> n IH. rewrite repeat_app. have ->: S n = n + 1 by lia. apply: (rt_trans (y := repeat sz n ++ [so] ++ [so])); last by (rewrite ?app_assoc; apply: multi_step_apprI). rewrite repeat_app -?app_assoc. apply /multi_step_applI /rt_step /stepI_nil. by eauto with in_srs_db nocore. Qed.
imports: List Relation_Operators Operators_Properties PeanoNat Lia ssreflect ssrbool ssrfun