intros a b; case a; case b; simpl in |- *; auto.
intros a0 m a1 m0; split; auto.
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (plusA (multA (invA a1) a0) A0);
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with
(plusA (multA (invA a1) a0) (plusA (multA a1 a0) (invA (multA a1 a0))));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with
(plusA (plusA (multA (invA a1) a0) (multA a1 a0)) (invA (multA a1 a0)));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (multA (plusA (invA a1) a1) a0) (invA (multA a1 a0)));
auto.
apply plusA_eqA_comp with (1 := cs); auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (multA a0 (invA a1)) (multA a0 a1));
auto.
apply (eqA_trans _ _ _ _ _ _ _ _ _ cs) with (multA a0 (plusA (invA a1) a1));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (multA (plusA a1 (invA a1)) a0) (invA (multA a1 a0)));
auto.
apply
(eqA_trans _ _ _ _ _ _ _ _ _ cs)
with (plusA (multA A0 a0) (invA (multA a1 a0)));
auto.
apply (eqA_sym _ _ _ _ _ _ _ _ _ cs); 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 mult_invTerm_com_r :
forall a b : Term, eqTerm (multTerm a (invTerm b)) (invTerm (multTerm a b)).