PROOF.balance.if.get: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 869-884 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=869&end_line=884

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.get(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~refl: Refl(~K, ~cmp), ~eq: Eq(~K, ~cmp),
  ~flip: Flip(~K, ~cmp), ~trans: Trans(~K, ~cmp),
  heavy_hi: Bool, heavy_lo: Bool, +lb: Maybe<&2, K>, +ub: Maybe<&2, K>, +x: K,
  +k: K, +v: V, +lo: O.OMap<K, V>, +hi: O.OMap<K, V>,
  el: {Laws.bounded(~K, ~V, ~cmp, lo, lb, Some{k}) == True{} : Bool},
  eh: {Laws.bounded(~K, ~V, ~cmp, hi, Some{k}, ub) == True{} : Bool}
) -> {g(~K, ~V, ~cmp, O.OMap.balance.if(K, V, heavy_hi, heavy_lo, k, v, lo, hi), x)
      == g(~K, ~V, ~cmp, O.OBin{0, k, v, lo, hi}, x) : Maybe<&2, V>}:
  match heavy_hi heavy_lo:
    case True{} _:
      rot_lo.get(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans, hi, ub, x, k, v, lo, eh)
    case False{} True{}:
      rot_hi.get(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans, lo, lb, x, k, v, hi, el)
    case False{} False{}:
      {==}

Uses (13):
  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=Eq
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Flip
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Refl
  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=g
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rot_hi.get
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rot_lo.get
  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