rewrite <- H.
ring.
Qed.

(* Specifications: *)
Lemma Lcp2 : forall a b c : F, a + b = c -> b = c - a.
intros.
Lemma Lcm1 : forall a b c : F, a - b = c -> a = c + b.
intros.
Lemma Lcm2 : forall a b c : F, a - b = c -> b = a - c.
intros.
Lemma Lcop1 : forall a b : F, - a = b -> a = - b.
intros.
Lemma Lcmult1 : forall a b c : F, b <> 0 -> a * b = c -> a = c / b.
intros; field_simplify_eq; auto.