Section Lemmas1_2.
auto with algebra.
Qed.
auto with algebra.
Qed.
intros.
apply Trans with (min f mX v); auto with algebra.
Qed.

Lemma vecspace_op_reg_l :
forall (f : F) (v : V),
~ f =' (zero F) in _ -> f mX v =' (zero V) in _ -> v =' (zero V) in _.