PROOF.del.bnd: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1165-1189 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=1165&end_line=1189

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.bnd(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
  t: O.OMap<K, V>, +lb: Maybe<&2, K>, +ub: Maybe<&2, K>, +k: K,
  +bt: {Laws.bounded(~K, ~V, ~cmp, t, lb, ub) == True{} : Bool}
) -> {Laws.bounded(~K, ~V, ~cmp, O.OMap.del(~K, ~V, ~cmp, t, k), lb, ub) == True{} : Bool}:
  match t:
    case O.OTip{}:
      {==}
    case O.OBin{+s, +key, +val, +lo, +hi}:
      +b_a = bn.a(~K, ~V, ~cmp, lb, ub, key, val, lo, hi, bt)
      +b_b = bn.b(~K, ~V, ~cmp, lb, ub, key, val, lo, hi, bt)
      +b_l = bn.l(~K, ~V, ~cmp, lb, ub, key, val, lo, hi, bt)
      +b_h = bn.h(~K, ~V, ~cmp, lb, ub, key, val, lo, hi, bt)
      cmp.split(O.OMap<K, V>, Bool, y => Laws.bounded(~K, ~V, ~cmp, y, lb, ub), True{},
        cmp(k, key),
        u => O.OMap.balance(K, V, key, val, O.OMap.del(~K, ~V, ~cmp, lo, k), hi),
        u => O.OMap.glue(K, V, lo, hi),
        u => O.OMap.balance(K, V, key, val, lo, O.OMap.del(~K, ~V, ~cmp, hi, k)),
        e => balance.bnd(~K, ~V, ~cmp, ~trans, lb, ub, key, val,
          O.OMap.del(~K, ~V, ~cmp, lo, k), hi, b_a, b_b,
          del.bnd(~K, ~V, ~cmp, ~trans, lo, lb, Some{key}, k, b_l), b_h),
        e => glue.bnd(~K, ~V, ~cmp, ~trans, hi, lo, lb, ub, key, b_a, b_b, b_l, b_h),
        e => balance.bnd(~K, ~V, ~cmp, ~trans, lb, ub, key, val, lo,
          O.OMap.del(~K, ~V, ~cmp, hi, k), b_a, b_b, b_l,
          del.bnd(~K, ~V, ~cmp, ~trans, hi, Some{key}, ub, k, b_h)))

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=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=bounded
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Trans
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=balance.bnd
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.a
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.b
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.h
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.l
  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.bnd
  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-kit-collections@0.1.4.1/omap.bend&name=OMap.balance
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap.del
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap.glue