PROOF.bal.hi: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1571-1584 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=1571&end_line=1584

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 bal.hi(
  -K: Data, -V: Data, +k: K, +v: V, +lo: O.OMap<K, V>, +hi: O.OMap<K, V>, +hi2: O.OMap<K, V>,
  +ok: {Laws.weight_ok(W(K, V, lo), W(K, V, hi)) == True{} : Bool},
  wbl: {WB(K, V, lo) == True{} : Bool},
  +pw: {PW(K, V, W(K, V, hi), hi2) == True{} : Bool}
) -> {PW(K, V, Nat.add(W(K, V, lo), W(K, V, hi)), Laws.g_balance(K, V, k, v, lo, hi2)) == True{} : Bool}:
  +a = W(K, V, lo)
  +c = W(K, V, hi)
  +c2 = W(K, V, hi2)
  +nr = MBool.eq_true_of_and_right(WB(K, V, hi2), Ord.near(c, c2), pw)
  +n1 = MBool.eq_true_of_and_left(Nat.is_le(c, 1n+c2), Nat.is_le(c2, 1n+c), nr)
  +n2 = MBool.eq_true_of_and_right(Nat.is_le(c, 1n+c2), Nat.is_le(c2, 1n+c), nr)
  MBool.and_eq_true(WB(K, V, Laws.g_balance(K, V, k, v, lo, hi2)), Ord.near(Nat.add(a, c), W(K, V, Laws.g_balance(K, V, k, v, lo, hi2))), bal.wb(K, V, k, v, lo, hi2, wbl, MBool.eq_true_of_and_left(WB(K, V, hi2), Ord.near(c, c2), pw),
      Ord.almhi.w0(a, c, c2, Ord.wok_l(a, c, ok), Ord.wok_r(a, c, ok), n1, n2)), bal.hi.near(K, V, k, v, lo, hi, hi2, n1, n2))

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
  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=bend-kit-collections@0.1.4.1/LAWS.bend&name=g_balance
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=weight_ok
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=PW
  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=bal.hi.near
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bal.wb
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=almhi.w0
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=near
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=wok_l
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=wok_r
  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