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 dvdp_exp_sub p q k l: p != 0 ->
(p ^+ k %| q * p ^+ l) = (p ^+ (k - l) %| q).