PROOF.rot_hi.single.bnd: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 390-405 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=390&end_line=405

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.single.bnd(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
  +lb: Maybe<&2, K>, +ub: Maybe<&2, K>, +k: K, +v: V, +lk: K, +lv: V,
  +ll: O.OMap<K, V>, +lh: 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.bin(K, V, lk, lv, ll, O.OMap.bin(K, V, k, v, lh, hi)), lb, ub) == True{} : Bool}:
  +l_b = bn.b(~K, ~V, ~cmp, lb, Some{k}, lk, lv, ll, lh, el)
  bn.i(~K, ~V, ~cmp, lb, ub, lk, lv, ll, O.OMap.bin(K, V, k, v, lh, hi),
    bn.a(~K, ~V, ~cmp, lb, Some{k}, lk, lv, ll, lh, el),
    below_trans(~K, ~cmp, ~trans, ub, lk, k, l_b, eb),
    bn.l(~K, ~V, ~cmp, lb, Some{k}, lk, lv, ll, lh, el),
    bn.i(~K, ~V, ~cmp, Some{lk}, ub, k, v, lh, hi, l_b, eb,
      bn.h(~K, ~V, ~cmp, lb, Some{k}, lk, lv, ll, lh, el), eh))

Uses (14):
  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=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/omap.bend&name=OMap
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap.bin