proposition: Lemma lastkey_ltn A a (h : natmap A) x : a < last_key h -> {in dom h, forall y, y < x} <-> last_key h < x.
proof: Proof. move/dom_lastkeyE=>D; split; first by apply. by move=>Y y X; apply: leq_ltn_trans Y; apply: lastkey_max. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path interval) pcm(options prelude pred finmap rtc seqext useqord uslice uconsec)