proposition: Lemma rclo3_dist clo (MON: monotone3 clo) (DIST: forall r1 r2, clo (r1 \3/ r2) <3= (clo r1 \3/ clo r2)): forall r1 r2, rclo3 clo (r1 \3/ r2) <3= (rclo3 clo r1 \3/ rclo3 clo r2).
proof: Proof. intros. induction PR. + destruct IN; [left|right]; apply rclo3_base, H. + assert (REL: clo (rclo3 clo r1 \3/ rclo3 clo r2) x0 x1 x2). { eapply MON. apply IN. apply H. } apply DIST in REL. destruct REL; [left|right]; apply rclo3_clo, H0. Qed.
imports: Program.Basics Paco(paco3 pacotac)