Section EUTTG_Properties1.
Context {E : Type -> Type} {R1 R2 : Type} (RR : R1 -> R2 -> Prop).
Local Notation euttG := (@euttG E R1 R2 RR).
Variant transL (r: itree E R1 -> itree E R2 -> Prop) (t1: itree E R1) (t2: itree E R2) : Prop :=
| transL_intro t' RR1
(EQL: eqit RR1 true true t1 t')
(EQR: r t' t2)
(LERR: forall x x' y, RR1 x x' -> RR x' y -> RR x y)
: transL r t1 t2
.
Hint Constructors transL.

Lemma transLleU: transL <3= transU RR.