proposition: Lemma isapartdectodeceq { X : hSet } ( R : apart X ) ( is : isapartdec R ) : isdeceq X.
proof: Proof. intros y z. destruct ( is y z ) as [ l | r ]. - apply ii2. intros f. apply ( pr1 ( pr2 R ) z). rewrite f in l. assumption. - apply ii1. assumption. Defined.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.PartA UniMath.Foundations.Propositions UniMath.Foundations.NaturalNumbers UniMath.Algebra.RigsAndRings UniMath.Algebra.Domains_and_Fields UniMath.NumberSystems.Integers UniMath.Algebra.Monoids