proposition: Lemma gpaco1_compat_init clo (CMP: compatible1 gf clo): gpaco1 gf clo bot1 bot1 <1= paco1 gf bot1.
proof: Proof. intros. destruct PR. revert x0 IN. pcofix CIH. intros. pstep. eapply gf_mon; [| right; apply CIH, rclo1_rclo, PR]. apply compat1_compat with (gf:=gf). apply rclo1_compat. apply gf_mon. apply CMP. eapply rclo1_mon. apply IN. intros. destruct PR; [|contradiction]. _punfold H; [..|apply gpaco1_def_mon, gf_mon]. eapply gpaco1_def_mon. apply gf_mon. apply H. intros. destruct PR; [|destruct H0; contradiction]. left. apply H0. Qed.
imports: Program.Basics Paco(paco1 pacotac)