proposition: Lemma sepit_cons x s f : sepit (x::s) f =p f x # sepit s f.
proof: Proof. move=>h; split. - case=>/=; case=>[|h0 hs]; case=>//= /eqP; rewrite eqSS =>/eqP Hs. rewrite /seqjoin big_cons =>->[H0 H1]. by exists h0, (seqjoin hs); do!split=>//; exists hs. case=>h1[_][{h}-> H1][hs][E -> H]. by exists (h1 :: hs); rewrite /= E /seqjoin !big_cons. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq bigop fintype finset) pcm(options axioms prelude seqperm pred seqext)