proposition: Lemma compatible'6_companion clo (RES: compatible'6 clo): clo <7= cpn6 gf.
proof: Proof. assert (MON: monotone6 gf'6). { econstructor. apply LE, IN. eapply gf_mon, LE. apply IN. } assert (CPN: clo <7= cpn6 gf'6). { intros. econstructor. apply RES. apply PR. } intros. apply CPN in PR. econstructor; [|apply PR]. econstructor; [apply cpn6_mon|]; intros. assert (PR1: cpn6 gf'6 (gf r) <6= cpn6 gf'6 (gf'6 (cpn6 gf r))). { intros. eapply cpn6_mon. apply PR1. intros. assert (TMP: gf (cpn6 gf r) <6= (cpn6 gf r /6\ gf (cpn6 gf r))). { split; [apply cpn6_step; [apply gf_mon|]|]; assumption. } apply TMP. eapply gf_mon. apply PR2. intros. apply cpn6_base; assumption. } apply PR1 in PR0. clear PR1. eapply compat6_compat with (gf:=gf'6) in PR0; [|apply cpn6_compat, MON]. eapply gf_mon; [apply PR0|]. intros. eapply cpn6_cpn; [apply MON|]. eapply cpn6_mon; [apply PR1|]. intros. econstructor; [|apply PR2]. apply compat6_compatible', cpn6_compat, gf_mon. Qed.
imports: Program.Basics Paco(paco6 pacotac)