PROOF.glue.bnd: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1149-1163 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=1149&end_line=1163

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 glue.bnd(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
  hi: O.OMap<K, V>, +lo: O.OMap<K, V>, +lb: Maybe<&2, K>, +ub: Maybe<&2, K>,
  +key: K,
  eka: {Laws.above(~K, ~cmp, lb, key) == True{} : Bool},
  ekb: {Laws.below(~K, ~cmp, ub, key) == True{} : Bool},
  el: {Laws.bounded(~K, ~V, ~cmp, lo, lb, Some{key}) == True{} : Bool},
  eh: {Laws.bounded(~K, ~V, ~cmp, hi, Some{key}, ub) == True{} : Bool}
) -> {Laws.bounded(~K, ~V, ~cmp, O.OMap.glue(K, V, lo, hi), lb, ub) == True{} : Bool}:
  match hi:
    case O.OTip{}:
      weaken_hi(~K, ~V, ~cmp, ~trans, lo, lb, key, ub, el, ekb)
    case O.OBin{s, +k, +v, +hl, +hh}:
      glue.fin.bnd(~K, ~V, ~cmp, ~trans, O.OMap.pop_min(K, V, hl, k, v, hh), lo, lb, ub, key,
        eka, el, pm.bnd(~K, ~V, ~cmp, ~trans, hl, Some{key}, ub, k, v, hh, eh))

Uses (13):
  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=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=glue.fin.bnd
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=pm.bnd
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=weaken_hi
  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.glue
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap.pop_min