proposition: Lemma cause_step_ext_cause_step: forall h l l' h', cause_step h l l' -> cause_step (h ++ h') l l'.
proof: Proof. intros. unfold cause_step in H. unfold cause_step. destruct H. left. open_conjs. split_all. apply prec_ext_prec. assumption. assumption. assumption. right. open_conjs. split_all. apply prec_ext_prec. assumption. assumption. assumption. assumption. assumption. Qed.
imports: Coq(FunctionalExtensionality Arith Lia) Coq(Arith.Peano_dec Arith.Compare_dec) Coq(Relations.Relation_Operators) Coq(List) Chapar(Predefs)