PROOF.balance.if.bnd: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 469-485 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=469&end_line=485

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 balance.if.bnd(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
  heavy_hi: Bool, heavy_lo: Bool, +lb: Maybe<&2, K>, +ub: Maybe<&2, K>, +k: K,
  +v: V, +lo: O.OMap<K, V>, +hi: O.OMap<K, V>,
  +ea: {Laws.above(~K, ~cmp, lb, k) == True{} : Bool},
  +eb: {Laws.below(~K, ~cmp, ub, k) == True{} : Bool},
  +el: {Laws.bounded(~K, ~V, ~cmp, lo, lb, Some{k}) == True{} : Bool},
  +eh: {Laws.bounded(~K, ~V, ~cmp, hi, Some{k}, ub) == True{} : Bool}
) -> {Laws.bounded(~K, ~V, ~cmp,
       O.OMap.balance.if(K, V, heavy_hi, heavy_lo, k, v, lo, hi), lb, ub) == True{} : Bool}:
  match heavy_hi heavy_lo:
    case True{} _:
      rot_lo.bnd(~K, ~V, ~cmp, ~trans, hi, lb, ub, k, v, lo, ea, eb, el, eh)
    case False{} True{}:
      rot_hi.bnd(~K, ~V, ~cmp, ~trans, lo, lb, ub, k, v, hi, ea, eb, el, eh)
    case False{} False{}:
      bn.i(~K, ~V, ~cmp, lb, ub, k, v, lo, hi, ea, eb, el, eh)

Uses (12):
  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=above
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=below
  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=bn.i
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rot_hi.bnd
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rot_lo.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.if