intros p q r s H'; generalize r s; elim H'; clear r s H'; auto.
intros x p0 r s H H0 H1; inversion H1.
intros H4; inversion H4; apply ltPO.
intros x y p0 q0 H r s H0 H1 H2 H3; inversion_clear H2; try discriminate;
inversion_clear H3; try discriminate; auto.
apply ltP_hd.
apply ltT_eqTl with (a := y); auto.
apply ltT_eqTr with (a := x); auto.
intros x y p0 q0 H H0 H1 r s H2 H3 H4 H5; inversion_clear H4;
try discriminate; inversion_clear H5; try discriminate.
apply ltP_tl; auto.
apply (eqT_trans A n) with (y := y); auto.
apply (eqT_trans A n) with (y := x); auto.
apply (eqT_sym A n); auto.
apply H1; auto.
apply canonical_imp_canonical with (a := x); auto.
apply canonical_imp_canonical with (a := y); auto.
Qed.

Theorem eqp_imp_canonical :
forall p q, eqP p q -> canonical A0 eqA ltM p -> canonical A0 eqA ltM q.