Section Porder.
Load "hCoefStructure".
Load "hOrderStructure".
Load "hTerm".
Set Implicit Arguments.
Unset Strict Implicit.
Definition ltT (a b : Term A n) : Prop := ltM (T2M a) (T2M b).
Hint Unfold ltT.
Set Strict Implicit.
Unset Implicit Arguments.
unfold transitive, ltT in |- *; auto.
intros x y z H' H'0; apply (ltM_trans _ _ _ _ os) with (y := T2M y); auto.
Qed.

Lemma eqT_compat_ltTr :
forall a b c : Term A n, eqT b c -> ltT a b -> ltT a c.