PROOF.glue.wb: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1666-1677 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=1666&end_line=1677

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 glue.wb(
  -K: Data, -V: Data, hi: O.OMap<K, V>, +lo: O.OMap<K, V>, -key: K, -val: V,
  +e: {WB(K, V, O.OBin{0, key, val, lo, hi}) == True{} : Bool}
) -> {PW(K, V, Nat.add(W(K, V, lo), W(K, V, hi)), Laws.g_glue(K, V, lo, hi)) == True{} : Bool}:
  match hi:
    case O.OTip{}:
      MBool.and_eq_true(WB(K, V, lo), Ord.near(Nat.add(W(K, V, lo), 1n), W(K, V, lo)), wb.l(K, V, key, val, lo, O.OTip{}, e), Ord.neargt.w0(W(K, V, lo)))
    case O.OBin{s, +k, +v, +hl, +hh}:
      +hi = {O.OBin{0, k, v, hl, hh} : O.OMap<K, V>}
      glue.fin.wb(K, V, Laws.g_pop_min(K, V, hl, k, v, hh), lo, hi,
        wb.ok(K, V, key, val, lo, hi, e), wb.l(K, V, key, val, lo, hi, e),
        pm.wb(K, V, hl, k, v, hh, wb.h(K, V, key, val, lo, hi, e)))

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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_glue
  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=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=glue.fin.wb
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=pm.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=neargt.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