proposition: Lemma geninvl : forall x : E, Equal (genlaw (geninv x) x) e.
proof: Proof. intros x; try assumption. apply Trans with (genlaw (genlaw (geninv x) x) e); auto with algebra. apply Trans with (genlaw (genlaw (geninv x) x) (genlaw (geninv x) (geninv (geninv x)))); auto with algebra. apply Trans with (genlaw (geninv x) (genlaw x (genlaw (geninv x) (geninv (geninv x))))); auto with algebra. apply Trans with (genlaw (geninv x) (genlaw (genlaw x (geninv x)) (geninv (geninv x)))); auto with algebra. apply Trans with (genlaw (geninv x) (genlaw e (geninv (geninv x)))); auto with algebra. apply Trans with (genlaw (genlaw (geninv x) e) (geninv (geninv x))); auto with algebra. apply Trans with (genlaw (geninv x) (geninv (geninv x))); auto with algebra. Qed.
imports: Sub_group Abelian_group_cat