Section Zup1.
Variable R : RING.
Hint Resolve Z_to_group_nat_eq_pos: algebra.
Hint Resolve Z_to_group_nat_unit: algebra.
Hint Resolve Zl1: algebra.
Hint Resolve Zl2: algebra.

Lemma nat_to_group_mult :
forall n m : nat,
Equal (nat_to_group (ring_unit R) (n * m))
(ring_mult (nat_to_group (ring_unit R) n) (nat_to_group (ring_unit R) m)).