Section EUTTG_principles.
Context {E : Type -> Type} {R1 R2 : Type} (RR : R1 -> R2 -> Prop).
Local Notation euttG := (@euttG E R1 R2 RR).
(* Make new hypotheses *)

Lemma euttG_cofix rH rL gL gH x
(OBG: forall gL' (INCL: gL <2= gL') (CIHL: x <2= gL') gH' (INCH: gH <2= gH') (CIHH: x <2= gH'), x <2= euttG rH rL gL' gH'):
x <2= euttG rH rL gL gH.