proposition: Lemma cause_in: forall h l l', cause h l l' -> (In l h /\ In l' h).
proof: Proof. intros. open_conjs. induction H. apply cause_step_in. assumption. open_conjs. split. assumption. assert (A:= cause_step_in h l' l'' H0). open_conjs. assumption. Qed.
imports: Coq(FunctionalExtensionality Arith Lia) Coq(Arith.Peano_dec Arith.Compare_dec) Coq(Relations.Relation_Operators) Coq(List) Chapar(Predefs)