PROOF.pm.wb: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1633-1644 of bend-kit-collections@0.1.4.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&start_line=1633&end_line=1644

import Base
import bend-mathlib@0.7.4.0/bool.bend as MBool
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws
import bend-kit-collections@0.1.4.1/omap.bend as O
import bend-kit-collections@0.1.4.1/nat_order.bend as Ord

def pm.wb(
  -K: Data, -V: Data, lo: O.OMap<K, V>, +k: K, +v: V, +hi: O.OMap<K, V>,
  +e: {WB(K, V, O.OBin{0, k, v, lo, hi}) == True{} : Bool}
) -> {PMW(K, V, Nat.add(W(K, V, lo), W(K, V, hi)), Laws.g_pop_min(K, V, lo, k, v, hi)) == True{} : Bool}:
  match lo:
    case O.OTip{}:
      MBool.and_eq_true(WB(K, V, hi), Ord.near(1n+W(K, V, hi), W(K, V, hi)), wb.h(K, V, k, v, O.OTip{}, hi, e), Ord.nearpm.w0(W(K, V, hi)))
    case O.OBin{s, +lk, +lv, +ll, +lh}:
      +lo = {O.OBin{0, lk, lv, ll, lh} : O.OMap<K, V>}
      pm.fin.wb(K, V, Laws.g_pop_min(K, V, ll, lk, lv, lh), k, v, lo, hi,
        wb.ok(K, V, k, v, lo, hi, e), wb.h(K, V, k, v, lo, hi, e),
        pm.wb(K, V, ll, lk, lv, lh, wb.l(K, V, k, v, lo, hi, e)))

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=g_pop_min
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=PMW
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=W
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=WB
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=pm.fin.wb
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=wb.h
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=wb.l
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=wb.ok
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=near
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=nearpm.w0
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=and_eq_true