proposition: Lemma hzqrandplusineq ( p : hz ) ( x : hzneq 0 p ) ( a c : hz ) : hzleh 0 ( hzremaindermod p x ( hzremaindermod p x a + hzremaindermod p x c ) ) × hzlth ( hzremaindermod p x ( hzremaindermod p x a + hzremaindermod p x c ) ) ( nattohz ( hzabsval p ) ).
proof: Proof. intros. split. - apply hzleh0remaindermod. - apply hzlthremaindermodmod. Defined.
imports: UniMath.PAdics.lemmas UniMath.NumberSystems.Integers UniMath.Foundations.Preamble