proposition: Lemma gpaco11_mon_gen (gf' clo clo': rel -> rel) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r r' rg rg' (IN: @gpaco11 gf clo r rg x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10) (gf_mon: monotone11 gf) (LEgf: gf <12= gf') (LEclo: clo <12= clo') (LEr: r <11= r') (LErg: rg <11= rg') : @gpaco11 gf' clo' r' rg' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10.
proof: Proof. eapply gpaco11_mon; [|apply LEr|apply LErg]. destruct IN. econstructor. eapply rclo11_mon_gen. apply IN. apply LEclo. intros. destruct PR; [| right; apply H]. left. eapply paco11_mon_gen. apply H. - intros. eapply LEgf. eapply gf_mon. apply PR. intros. eapply rclo11_mon_gen. apply PR0. apply LEclo. intros; apply PR1. - intros. apply PR. Qed.
imports: Program.Basics Paco(paco11 pacotac)