proposition: Lemma gpaco10_mon_gen (gf' clo clo': rel -> rel) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r r' rg rg' (IN: @gpaco10 gf clo r rg x0 x1 x2 x3 x4 x5 x6 x7 x8 x9) (gf_mon: monotone10 gf) (LEgf: gf <11= gf') (LEclo: clo <11= clo') (LEr: r <10= r') (LErg: rg <10= rg') : @gpaco10 gf' clo' r' rg' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9.
proof: Proof. eapply gpaco10_mon; [|apply LEr|apply LErg]. destruct IN. econstructor. eapply rclo10_mon_gen. apply IN. apply LEclo. intros. destruct PR; [| right; apply H]. left. eapply paco10_mon_gen. apply H. - intros. eapply LEgf. eapply gf_mon. apply PR. intros. eapply rclo10_mon_gen. apply PR0. apply LEclo. intros; apply PR1. - intros. apply PR. Qed.
imports: Program.Basics Paco(paco10 pacotac)