proposition: Lemma umPtUPtE (k1 k2 : K) (v1 v2 : V) f : (k1 \\-> v1 \+ f == k2 \\-> v2) = [&& k1 == k2, v1 == v2 & unitb f].
proof: Proof. apply/idP/idP; last first. - by case/and3P=>/eqP -> /eqP -> /unitbP ->; rewrite unitR. move/eqP/(um_prime _); case=>//; case. - move/(cancelPt2 _); rewrite validPt=>/(_ (erefl _)). by case=>->->->; rewrite !eq_refl unitb0. by move/unitbP; rewrite um_unitbPt. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path bigop) pcm(options prelude finmap seqperm pred seqext) pcm(pcm morphism)