intros a b; case a; case b; simpl in |- *; auto.
intros a0 m a1 m0; split; auto.
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (plusA (multA a1 (invA a0)) A0);
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with
(plusA (multA a1 (invA a0)) (plusA (multA a1 a0) (invA (multA a1 a0))));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with
(plusA (plusA (multA a1 (invA a0)) (multA a1 a0)) (invA (multA a1 a0)));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (multA a1 (plusA (invA a0) a0)) (invA (multA a1 a0)));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (multA a1 (plusA a0 (invA a0))) (invA (multA a1 a0)));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (multA a1 A0) (invA (multA a1 a0)));
auto.
apply (eqA_sym _ _ _ _ _ _ _ _ _ cs); auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (multA A0 a1) (invA (multA a1 a0)));
auto.
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (plusA A0 (invA (multA a1 a0)));
auto.
apply (eqA_sym _ _ _ _ _ _ _ _ _ cs);
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (plusA (invA (multA a1 a0)) A0);
auto.
Qed.

Theorem eqTerm_invTerm_comp :
forall a b : Term, eqTerm a b -> eqTerm (invTerm a) (invTerm b).