PROOF.rh.w: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1516-1522 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=1516&end_line=1522

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 rh.w(-K: Data, -V: Data, lo: O.OMap<K, V>, -k: K, -v: V, +hi: O.OMap<K, V>)
  -> {Nat.add(W(K, V, lo), W(K, V, hi)) == W(K, V, Laws.g_rot_hi(K, V, k, v, lo, hi)) : Nat}:
  match lo:
    case O.OTip{}:
      {==}
    case O.OBin{s, lk, lv, +ll, +lh}:
      rhp.w(K, V, Nat.is_lt(W(K, V, lh), Nat.mul(2n, W(K, V, ll))), k, v, lk, lv, ll, lh, hi)

Uses (8):
  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=rhp.w
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap