PROOF.rot_hi.double.bnd: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 407-434 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=407&end_line=434

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 rot_hi.double.bnd(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
  lh: O.OMap<K, V>, +lb: Maybe<&2, K>, +ub: Maybe<&2, K>, +k: K, +v: V,
  +lk: K, +lv: V, +ll: O.OMap<K, V>, +hi: O.OMap<K, V>,
  +eb: {Laws.below(~K, ~cmp, ub, k) == True{} : Bool},
  +el: {Laws.bounded(~K, ~V, ~cmp, O.OBin{0, lk, lv, ll, lh}, lb, Some{k}) == True{} : Bool},
  eh: {Laws.bounded(~K, ~V, ~cmp, hi, Some{k}, ub) == True{} : Bool}
) -> {Laws.bounded(~K, ~V, ~cmp,
       O.OMap.rot_hi.double(K, V, k, v, lk, lv, ll, lh, hi), lb, ub) == True{} : Bool}:
  match lh:
    case O.OTip{}:
      rot_hi.single.bnd(~K, ~V, ~cmp, ~trans, lb, ub, k, v, lk, lv, ll, O.OTip{}, hi,
        eb, el, eh)
    case O.OBin{s, +mk, +mv, +ml, +mh}:
      +lh = {O.OBin{0, mk, mv, ml, mh} : O.OMap<K, V>}
      +l_a = bn.a(~K, ~V, ~cmp, lb, Some{k}, lk, lv, ll, lh, el)
      +l_h = bn.h(~K, ~V, ~cmp, lb, Some{k}, lk, lv, ll, lh, el)
      +m_a = bn.a(~K, ~V, ~cmp, Some{lk}, Some{k}, mk, mv, ml, mh, l_h)
      +m_b = bn.b(~K, ~V, ~cmp, Some{lk}, Some{k}, mk, mv, ml, mh, l_h)
      bn.i(~K, ~V, ~cmp, lb, ub, mk, mv, O.OMap.bin(K, V, lk, lv, ll, ml),
        O.OMap.bin(K, V, k, v, mh, hi),
        above_trans(~K, ~cmp, ~trans, lb, lk, mk, l_a, m_a),
        below_trans(~K, ~cmp, ~trans, ub, mk, k, m_b, eb),
        bn.i(~K, ~V, ~cmp, lb, Some{mk}, lk, lv, ll, ml, l_a, m_a,
          bn.l(~K, ~V, ~cmp, lb, Some{k}, lk, lv, ll, lh, el),
          bn.l(~K, ~V, ~cmp, Some{lk}, Some{k}, mk, mv, ml, mh, l_h)),
        bn.i(~K, ~V, ~cmp, Some{mk}, ub, k, v, mh, hi, m_b, eb,
          bn.h(~K, ~V, ~cmp, Some{lk}, Some{k}, mk, mv, ml, mh, l_h), eh))

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=below
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=bounded
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Trans
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=above_trans
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=below_trans
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.a
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.b
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.h
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.i
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=bn.l
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rot_hi.single.bnd
  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-kit-collections@0.1.4.1/omap.bend&name=OMap.bin
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap.rot_hi.double