PROOF.rot_lo.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 311-326 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=311&end_line=326

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_lo.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, +lo: O.OMap<K, V>,
  +hk: K, +hv: V, +hl: O.OMap<K, V>, +hh: O.OMap<K, V>,
  +ea: {Laws.above(~K, ~cmp, lb, k) == True{} : Bool},
  el: {Laws.bounded(~K, ~V, ~cmp, lo, lb, Some{k}) == True{} : Bool},
  +eh: {Laws.bounded(~K, ~V, ~cmp, O.OBin{0, hk, hv, hl, hh}, Some{k}, ub) == True{} : Bool}
) -> {Laws.bounded(~K, ~V, ~cmp,
       O.OMap.bin(K, V, hk, hv, O.OMap.bin(K, V, k, v, lo, hl), hh), lb, ub) == True{} : Bool}:
  +h_a = bn.a(~K, ~V, ~cmp, Some{k}, ub, hk, hv, hl, hh, eh)
  bn.i(~K, ~V, ~cmp, lb, ub, hk, hv, O.OMap.bin(K, V, k, v, lo, hl), hh,
    above_trans(~K, ~cmp, ~trans, lb, k, hk, ea, h_a),
    bn.b(~K, ~V, ~cmp, Some{k}, ub, hk, hv, hl, hh, eh),
    bn.i(~K, ~V, ~cmp, lb, Some{hk}, k, v, lo, hl, ea, h_a, el,
      bn.l(~K, ~V, ~cmp, Some{k}, ub, hk, hv, hl, hh, eh)),
    bn.h(~K, ~V, ~cmp, Some{k}, ub, hk, hv, hl, hh, 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=above
  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=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