PROOF.glue.fin.bnd.go: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1117-1134 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=1117&end_line=1134

import Base
import bend-mathlib@0.7.4.0/bool.bend as MBool
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.fin.bnd.go(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
  +mk: K, +mv: V, +t: 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},
  el: {Laws.bounded(~K, ~V, ~cmp, lo, lb, Some{key}) == True{} : Bool},
  +pmr: {PM(~K, ~V, ~cmp, Some{key}, ub, {(mk, mv, t) : K & V & O.OMap<K, V>}) == True{} : Bool}
) -> {Laws.bounded(~K, ~V, ~cmp,
       O.OMap.glue.fin(K, V, lo, {(mk, mv, t) : K & V & O.OMap<K, V>}), lb, ub) == True{} : Bool}:
  +ab = Bool.and(Laws.above(~K, ~cmp, Some{key}, mk), Laws.below(~K, ~cmp, ub, mk))
  +c = Laws.bounded(~K, ~V, ~cmp, t, Some{mk}, ub)
  +eab = MBool.eq_true_of_and_left(ab, c, pmr)
  +km = MBool.eq_true_of_and_left(Laws.above(~K, ~cmp, Some{key}, mk), Laws.below(~K, ~cmp, ub, mk), eab)
  balance.bnd(~K, ~V, ~cmp, ~trans, lb, ub, mk, mv, lo, t,
    above_trans(~K, ~cmp, ~trans, lb, key, mk, eka, km),
    MBool.eq_true_of_and_right(Laws.above(~K, ~cmp, Some{key}, mk), Laws.below(~K, ~cmp, ub, mk), eab),
    weaken_hi(~K, ~V, ~cmp, ~trans, lo, lb, key, Some{mk}, el, km),
    MBool.eq_true_of_and_right(ab, c, pmr))

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  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=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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=PM
  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=balance.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.fin
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_left
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_right