proposition: Lemma commringquotprandop1 { A : commring } ( R : @ringeqrel A ) ( a b : A ) : @op1 ( commringquot R ) ( setquotpr ( pr1 R ) a ) ( setquotpr ( pr1 R ) b ) = setquotpr ( pr1 R ) ( a + b ).
proof: Proof. intros. change ( @op1 ( commringquot R ) ) with ( setquotfun2 R R ( @op1 A ) ( pr1 ( iscomp2binoptransrel ( pr1 R ) ( eqreltrans _ ) ( pr2 R ) ) ) ). unfold setquotfun2. rewrite setquotuniv2comm. apply idpath. Defined.
imports: UniMath.PAdics.lemmas UniMath.PAdics.fps UniMath.PAdics.frac UniMath.PAdics.z_mod_p UniMath.NumberSystems.Integers