proposition: Lemma big_dom_seq (xs : seq I) : dom (\big[PCM.join/Unit]_(i <- xs) g i) =i if valid (\big[PCM.join/Unit]_(i <- xs) g i) then \big[cat/[::]]_(i <- xs) dom (g i) else [::].
proof: Proof. by move=>x; rewrite big_valid_dom_seq. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path bigop) pcm(options prelude finmap seqperm pred seqext) pcm(pcm morphism)