Section IDomainPseudoDivision.
Variable R : idomainType.
Implicit Type p q r d m n : {poly R}.
Hint Resolve divp0 divp1 mod0p modp0 modp1 : core.
Hint Resolve dvdp0 : core.
Hint Resolve dvdpp : core.

Lemma eqp_eq p q: p %= q -> (lead_coef q) *: p = (lead_coef p) *: q.