Section MonicDivisor.
Variable R : idomainType.
Variable q : {poly R}.
Hypothesis monq : q \is monic.
Implicit Type p d r : {poly R}.

Lemma ucl_eqp_eq p q : lead_coef q \is a GRing.unit ->
p %= q -> p = (lead_coef p / lead_coef q) *: q.