PROOF.rot_hi.double.get: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 817-833 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=817&end_line=833

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.double.get(
  ~K: Data, ~V: Data, ~cmp: K -> K -> Cmp, ~refl: Refl(~K, ~cmp), ~eq: Eq(~K, ~cmp),
  ~flip: Flip(~K, ~cmp), ~trans: Trans(~K, ~cmp),
  lh: O.OMap<K, V>, +x: K, +k: K, +v: V, +lk: K, +lv: V, +ll: O.OMap<K, V>,
  +hi: O.OMap<K, V>, +lkk: {cmp(lk, k) == LT{} : Cmp},
  +l_h: {Laws.bounded(~K, ~V, ~cmp, lh, Some{lk}, Some{k}) == True{} : Bool}
) -> {g(~K, ~V, ~cmp, O.OMap.rot_hi.double(K, V, k, v, lk, lv, ll, lh, hi), x)
      == g(~K, ~V, ~cmp, O.OBin{0, k, v, O.OBin{0, lk, lv, ll, lh}, hi}, x) : Maybe<&2, V>}:
  match lh:
    case O.OTip{}:
      rot_hi.single.get(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans, x, k, v, lk, lv, ll,
        O.OTip{}, hi, lkk)
    case O.OBin{s, +mk, +mv, +ml, +mh}:
      rot_hi.double.get2(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans, x, k, v, lk, lv, ll,
        mk, mv, ml, mh, hi,
        lt_of(cmp(lk, mk), bn.a(~K, ~V, ~cmp, Some{lk}, Some{k}, mk, mv, ml, mh, l_h)),
        lt_of(cmp(mk, k), bn.b(~K, ~V, ~cmp, Some{lk}, Some{k}, mk, mv, ml, mh, l_h)))

Uses (16):
  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=bounded
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Eq
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Flip
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Refl
  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=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=g
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=lt_of
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rot_hi.double.get2
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rot_hi.single.get
  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.rot_hi.double