proposition: Lemma domPtUnK k v f : valid (pts k v \+ f) -> all (ord k) (dom f) -> dom (pts k v \+ f) = k :: dom f.
proof: Proof. move=>W H; apply: ord_sorted_eq=>//=. - by rewrite path_min_sorted //; apply: sorted_dom. by move=>x; rewrite domPtUn !inE W eq_sym. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path bigop) pcm(options prelude finmap seqperm pred seqext) pcm(pcm morphism)