intros a b c eqT1.
apply eqTerm_trans with (y := multTerm (plusTerm a (invTerm b)) c); auto.
apply
eqTerm_trans with (y := plusTerm (multTerm a c) (multTerm (invTerm b) c));
auto.
apply
eqTerm_trans with (y := plusTerm (multTerm a c) (invTerm (multTerm b c)));
auto.
apply eqTerm_minusTerm_plusTerm_invTerm; auto.
apply eqTerm_plusTerm_comp; auto.
apply eqT_trans with (y := multTerm b c); auto.
apply multTerm_eqT; auto.
apply invTerm_eqT; auto.
apply multTerm_eqT; auto.
apply eqT_trans with (y := b); auto.
apply invTerm_eqT; auto.
apply eqTerm_refl; auto.
apply eqTerm_sym; apply mult_invTerm_com; auto.
apply multTerm_plusTerm_dist_l; auto.
apply eqTerm_multTerm_comp; auto.
apply eqTerm_sym; apply eqTerm_minusTerm_plusTerm_invTerm; auto.
apply eqTerm_refl; auto.
Qed.
Hint Resolve multTerm_minusTerm_dist_l.

Theorem nzeroP_multTerm :
forall a b : Term, ~ zeroP a -> ~ zeroP b -> ~ zeroP (multTerm a b).