Section Lemmas1.
Variable K : FIELD.
Definition field_inverse (x : K) : K := Ap (field_inverse_map K) x.
Definition field_div (x y : K) : K := ring_mult x (field_inverse y).
exact (field_inverse_r_prf K).
Qed.
exact (field_inverse_l_prf K).
Qed.
exact (field_unit_non_zero K).
Qed.

Lemma FIELD_comp :
forall x x' : K, Equal x x' -> Equal (field_inverse x) (field_inverse x').