PROOF.put.wb: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1586-1606 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=1586&end_line=1606

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 put.wb(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, t: O.OMap<K, V>, +k: K, +v: V,
  +wb: {WB(K, V, t) == True{} : Bool}
) -> {PW(K, V, W(K, V, t), Laws.g_put(~K, ~V, ~cmp, t, k, v)) == 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_put(~K, ~V, ~cmp, lo, k, v), hi),
        u => O.OBin{s, key, v, lo, hi},
        u => Laws.g_balance(K, V, key, val, lo, Laws.g_put(~K, ~V, ~cmp, hi, k, v)),
        e => bal.lo(K, V, key, val, lo, Laws.g_put(~K, ~V, ~cmp, lo, k, v), hi, ok, wbh,
          put.wb(~K, ~V, ~cmp, lo, k, v, wbl)),
        e => MBool.and_eq_true(WB(K, V, O.OBin{s, key, v, lo, hi}), Ord.near(n, n), wb, Ord.nearrf.w0(n)),
        e => bal.hi(K, V, key, val, lo, hi, Laws.g_put(~K, ~V, ~cmp, hi, k, v), ok, wbl,
          put.wb(~K, ~V, ~cmp, hi, k, v, wbh)))

Uses (18):
  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_put
  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=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=nearrf.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