PROOF.weaken_hi: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1043-1060 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=1043&end_line=1060

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

# A tree bounded above by a is bounded above by anything above a.
def weaken_hi(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~trans: Trans(~K, ~cmp),
  t: O.OMap<K, V>, +lb: Maybe<&2, K>, +a: K, +ub: Maybe<&2, K>,
  +e: {Laws.bounded(~K, ~V, ~cmp, t, lb, Some{a}) == True{} : Bool},
  +eab: {Laws.below(~K, ~cmp, ub, a) == True{} : Bool}
) -> {Laws.bounded(~K, ~V, ~cmp, t, lb, ub) == True{} : Bool}:
  match t:
    case O.OTip{}:
      {==}
    case O.OBin{s, +k, +v, +lo, +hi}:
      bn.i(~K, ~V, ~cmp, lb, ub, k, v, lo, hi,
        bn.a(~K, ~V, ~cmp, lb, Some{a}, k, v, lo, hi, e),
        below_trans(~K, ~cmp, ~trans, ub, k, a,
          bn.b(~K, ~V, ~cmp, lb, Some{a}, k, v, lo, hi, e), eab),
        bn.l(~K, ~V, ~cmp, lb, Some{a}, k, v, lo, hi, e),
        weaken_hi(~K, ~V, ~cmp, ~trans, hi, Some{k}, a, ub,
          bn.h(~K, ~V, ~cmp, lb, Some{a}, k, v, lo, hi, e), eab))

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=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