proposition: Lemma lastkeyUn_mono A (h1 h2 : natmap A) t : valid (h1 \+ h2) -> last_key (h1 \+ h2) < t -> last_key h1 < t.
proof: Proof. move=>V; apply/leq_trans/lastkey_mono. by move=>x D; rewrite domUn inE V D. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path interval) pcm(options prelude pred finmap rtc seqext useqord uslice uconsec)