intros a b c nZc; apply eqA_trans with (y := divA (multA b a) c nZc); auto.
apply eqA_trans with (y := multA (divA b c nZc) a); auto.
apply divA_multA_comp_r with (1 := cs); auto.
Qed.
Hint Resolve divA_multA_comp_l.

Theorem invA_is_invA1 : forall a : A, eqA (invA a) (multA (invA A1) a).
intros a; apply eqA_trans with (y := plusA (invA a) A0); auto.