proposition: Lemma umfilt_leUn A (h1 h2 : natmap A) t : valid (h1 \+ h2) -> t <= last_key h1 -> {in dom h2, forall k, k > last_key h1} -> um_filter (le t) (h1 \+ h2) = um_filter (le t) h1.
proof: Proof. move=>V K D; rewrite umfiltUn // (umfilt_le0 (validR V)) ?unitR //. by move=>k /D /(leq_ltn_trans K). Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path interval) pcm(options prelude pred finmap rtc seqext useqord uslice uconsec)