proposition: Lemma rclo12_dist clo (MON: monotone12 clo) (DIST: forall r1 r2, clo (r1 \12/ r2) <12= (clo r1 \12/ clo r2)): forall r1 r2, rclo12 clo (r1 \12/ r2) <12= (rclo12 clo r1 \12/ rclo12 clo r2).
proof: Proof. intros. induction PR. + destruct IN; [left|right]; apply rclo12_base, H. + assert (REL: clo (rclo12 clo r1 \12/ rclo12 clo r2) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11). { eapply MON. apply IN. apply H. } apply DIST in REL. destruct REL; [left|right]; apply rclo12_clo, H0. Qed.
imports: Program.Basics Paco(paco12 pacotac)