PROOF.bif.wb: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1434-1452 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=1434&end_line=1452

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 bif.wb(
  -K: Data, -V: Data, heavy_hi: Bool, heavy_lo: Bool, +k: K, +v: V,
  +lo: O.OMap<K, V>, +hi: O.OMap<K, V>,
  eh: {Laws.g_heavy_hi(K, V, lo, hi) == heavy_hi : Bool},
  el: {Laws.g_heavy_lo(K, V, lo, hi) == heavy_lo : Bool},
  wbl: {WB(K, V, lo) == True{} : Bool}, wbh: {WB(K, V, hi) == True{} : Bool},
  +alm: {Ord.alm(W(K, V, lo), W(K, V, hi)) == True{} : Bool}
) -> {WB(K, V, Laws.g_balance.if(K, V, heavy_hi, heavy_lo, k, v, lo, hi)) == True{} : Bool}:
  match heavy_hi heavy_lo:
    case True{} _:
      rl.wb(K, V, hi, k, v, lo, wbl, wbh,
        Ord.gt_le(W(K, V, hi), Nat.mul(3n, W(K, V, lo)), eh), MBool.eq_true_of_and_left(Nat.is_le(W(K, V, hi), Nat.add(3n, Nat.mul(3n, W(K, V, lo)))), Nat.is_le(W(K, V, lo), Nat.add(3n, Nat.mul(3n, W(K, V, hi)))), alm))
    case False{} True{}:
      rh.wb(K, V, lo, k, v, hi, wbl, wbh,
        Ord.gt_le(W(K, V, lo), Nat.mul(3n, W(K, V, hi)), el), MBool.eq_true_of_and_right(Nat.is_le(W(K, V, hi), Nat.add(3n, Nat.mul(3n, W(K, V, lo)))), Nat.is_le(W(K, V, lo), Nat.add(3n, Nat.mul(3n, W(K, V, hi)))), alm))
    case False{} False{}:
      wb.i(K, V, k, v, lo, hi,
        MBool.and_eq_true(Nat.is_le(W(K, V, hi), Nat.mul(3n, W(K, V, lo))), Nat.is_le(W(K, V, lo), Nat.mul(3n, W(K, V, hi))), Ord.ngt_le(W(K, V, hi), Nat.mul(3n, W(K, V, lo)), eh), Ord.ngt_le(W(K, V, lo), Nat.mul(3n, W(K, V, hi)), el)),
        wbl, wbh)

Uses (19):
  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=Base/base.bend&name=Nat.is_le
  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_balance.if
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=g_heavy_hi
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=g_heavy_lo
  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=rh.wb
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rl.wb
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=wb.i
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=alm
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=gt_le
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=ngt_le
  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
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_left
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_right