proposition: Lemma gpaco3_compat_init clo (CMP: compatible3 gf clo): gpaco3 gf clo bot3 bot3 <3= paco3 gf bot3.
proof: Proof. intros. destruct PR. revert x0 x1 x2 IN. pcofix CIH. intros. pstep. eapply gf_mon; [| right; apply CIH, rclo3_rclo, PR]. apply compat3_compat with (gf:=gf). apply rclo3_compat. apply gf_mon. apply CMP. eapply rclo3_mon. apply IN. intros. destruct PR; [|contradiction]. _punfold H; [..|apply gpaco3_def_mon, gf_mon]. eapply gpaco3_def_mon. apply gf_mon. apply H. intros. destruct PR; [|destruct H0; contradiction]. left. apply H0. Qed.
imports: Program.Basics Paco(paco3 pacotac)