proposition: Lemma compatible'14_companion clo (RES: compatible'14 clo): clo <15= cpn14 gf.
proof: Proof. assert (MON: monotone14 gf'14). { econstructor. apply LE, IN. eapply gf_mon, LE. apply IN. } assert (CPN: clo <15= cpn14 gf'14). { intros. econstructor. apply RES. apply PR. } intros. apply CPN in PR. econstructor; [|apply PR]. econstructor; [apply cpn14_mon|]; intros. assert (PR1: cpn14 gf'14 (gf r) <14= cpn14 gf'14 (gf'14 (cpn14 gf r))). { intros. eapply cpn14_mon. apply PR1. intros. assert (TMP: gf (cpn14 gf r) <14= (cpn14 gf r /14\ gf (cpn14 gf r))). { split; [apply cpn14_step; [apply gf_mon|]|]; assumption. } apply TMP. eapply gf_mon. apply PR2. intros. apply cpn14_base; assumption. } apply PR1 in PR0. clear PR1. eapply compat14_compat with (gf:=gf'14) in PR0; [|apply cpn14_compat, MON]. eapply gf_mon; [apply PR0|]. intros. eapply cpn14_cpn; [apply MON|]. eapply cpn14_mon; [apply PR1|]. intros. econstructor; [|apply PR2]. apply compat14_compatible', cpn14_compat, gf_mon. Qed.
imports: Program.Basics Paco(paco14 pacotac)