intros a0 m; split; auto.
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (plusA a0 A0); auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA a0 (plusA (invA a0) (invA (invA a0))));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (plusA a0 (invA a0)) (invA (invA a0)));
auto.
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (plusA A0 (invA (invA a0))); auto.
apply (eqA_sym _ _ _ _ _ _ _ _ _ cs); auto.
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (plusA (invA (invA a0)) A0); auto.
apply (eqA_sym _ _ _ _ _ _ _ _ _ cs); auto.
Qed.

Theorem nZero_invTerm_nZero :
forall a : Term, ~ zeroP a -> ~ zeroP (invTerm a).