proposition: Lemma sc_succ : substitution_closed succ.
proof: Proof. intros t u s h. unfold succ, transp, Rof. set (k:=max(maxvar t)(maxvar u)). rewrite term_of_aterm_sub with (k:=S k). 2: apply le_n_S; apply Nat.le_max_r. rewrite term_of_aterm_sub with (k:=S k). 2: apply le_n_S; apply Nat.le_max_l. apply rpo_subst. hyp. Qed.
imports: CoLoR(LogicUtil ATerm VecUtil) CoLoR(term_spec EqUtil) CoLoR(NatUtil) Coq(List Relations) CoLoR(term SN ASubstitution) CoLoR(rpo rpo_extension) CoLoR(ARedPair ARelation RelUtil BoolUtil)