PROOF.del.wb: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1679-1699 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=1679&end_line=1699

import Base
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws
import bend-kit-collections@0.1.4.1/omap.bend as O

def del.wb(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, t: O.OMap<K, V>, +k: K,
  +wb: {WB(K, V, t) == True{} : Bool}
) -> {PW(K, V, W(K, V, t), Laws.g_del(~K, ~V, ~cmp, t, k)) == True{} : Bool}:
  match t:
    case O.OTip{}:
      {==}
    case O.OBin{+s, +key, +val, +lo, +hi}:
      +ok = wb.ok(K, V, key, val, lo, hi, wb)
      +wbl = wb.l(K, V, key, val, lo, hi, wb)
      +wbh = wb.h(K, V, key, val, lo, hi, wb)
      +n = Nat.add(W(K, V, lo), W(K, V, hi))
      cmp.split(O.OMap<K, V>, Bool, x => PW(K, V, n, x), True{}, cmp(k, key),
        u => Laws.g_balance(K, V, key, val, Laws.g_del(~K, ~V, ~cmp, lo, k), hi),
        u => Laws.g_glue(K, V, lo, hi),
        u => Laws.g_balance(K, V, key, val, lo, Laws.g_del(~K, ~V, ~cmp, hi, k)),
        e => bal.lo(K, V, key, val, lo, Laws.g_del(~K, ~V, ~cmp, lo, k), hi, ok, wbh,
          del.wb(~K, ~V, ~cmp, lo, k, wbl)),
        e => glue.wb(K, V, hi, lo, key, val, wb),
        e => bal.hi(K, V, key, val, lo, hi, Laws.g_del(~K, ~V, ~cmp, hi, k), ok, wbl,
          del.wb(~K, ~V, ~cmp, hi, k, wbh)))

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  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_balance
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=g_del
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=g_glue
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=PW
  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=bal.hi
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bal.lo
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=cmp.split
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=glue.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/omap.bend&name=OMap