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 root_bigmul x (ps : seq {poly R}) :
~~root (\big[*%R/1]_(p <- ps) p) x = all (fun p => ~~ root p x) ps.