proposition: Lemma hzqrandremainderq ( m : hz ) ( is : hzneq 0 m ) ( n : hz ) : 0 = hzquotientmod m is ( hzremaindermod m is n ).
proof: Proof. intros. apply ( hzqrtestq m is ( hzremaindermod m is n ) 0 ( hzremaindermod m is n ) ). split. - apply hzqrandremaindereq. - apply hzqrandremainderineq. Defined.
imports: UniMath.PAdics.lemmas UniMath.NumberSystems.Integers UniMath.Foundations.Preamble