PROOF.rh.wb: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1421-1432 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=1421&end_line=1432

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
import bend-kit-collections@0.1.4.1/nat_order.bend as Ord

def rh.wb(
  -K: Data, -V: Data, lo: O.OMap<K, V>, +k: K, +v: V, +hi: O.OMap<K, V>,
  +wbl: {WB(K, V, lo) == True{} : Bool}, wbh: {WB(K, V, hi) == True{} : Bool},
  heavy: Ord.LE(1n+Nat.mul(3n, W(K, V, hi)), W(K, V, lo)),
  alm: Ord.LE(W(K, V, lo), Nat.add(3n, Nat.mul(3n, W(K, V, hi))))
) -> {WB(K, V, Laws.g_rot_hi(K, V, k, v, lo, hi)) == True{} : Bool}:
  match lo:
    case O.OTip{}:
      Empty.absurd({WB(K, V, Laws.g_rot_hi(K, V, k, v, O.OTip{}, hi)) == True{} : Bool}, Ord.tiph(W(K, V, hi), heavy, w_pos(K, V, hi)))
    case O.OBin{s, +lk, +lv, +ll, +lh}:
      rhp.wb(K, V, Nat.is_lt(W(K, V, lh), Nat.mul(2n, W(K, V, ll))), k, v, lk, lv, ll, lh, hi,
        {==}, wbl, wbh, heavy, alm)

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=g_rot_hi
  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=rhp.wb
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=w_pos
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=LE
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=tiph
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap