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.
unfold eqT in |- *; unfold ltT in |- *; intros a b c H; rewrite H; auto.
Qed.
unfold eqT in |- *; unfold ltT in |- *; intros a b c H; rewrite H; auto.
Qed.
intros x y; unfold eqT in |- *; simpl in |- *; auto.
apply eqmon_dec.
Qed.

Theorem ltT_dec : forall x y : Term A n, {ltT x y} + {ltT y x} + {eqT x y}.