PROOF.bal.lo.near: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1541-1546 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=1541&end_line=1546

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 bal.lo.near(
  -K: Data, -V: Data, -k: K, -v: V, +lo: O.OMap<K, V>, +lo2: O.OMap<K, V>, +hi: O.OMap<K, V>,
  n1: Ord.LE(W(K, V, lo), 1n+W(K, V, lo2)), n2: Ord.LE(W(K, V, lo2), 1n+W(K, V, lo))
) -> {Ord.near(Nat.add(W(K, V, lo), W(K, V, hi)), W(K, V, Laws.g_balance(K, V, k, v, lo2, hi))) == True{} : Bool}:
  %bal.w(K, V, k, v, lo2, hi) : {Ord.near(Nat.add(W(K, V, lo), W(K, V, hi)), _) == True{} : Bool}
  Ord.nearlo.w0(W(K, V, lo), W(K, V, lo2), W(K, V, hi), n1, n2)

Uses (10):
  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=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/PROOF.bend&name=W
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bal.w
  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=near
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=nearlo.w0
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap