PROOF.rot_lo.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 695-711 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=695&end_line=711

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.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),
  hl: O.OMap<K, V>, +x: K, +k: K, +v: V, +lo: O.OMap<K, V>, +hk: K, +hv: V,
  +hh: O.OMap<K, V>, +khk: {cmp(k, hk) == LT{} : Cmp},
  +h_l: {Laws.bounded(~K, ~V, ~cmp, hl, Some{k}, Some{hk}) == True{} : Bool}
) -> {g(~K, ~V, ~cmp, O.OMap.rot_lo.double(K, V, k, v, lo, hk, hv, hl, hh), x)
      == g(~K, ~V, ~cmp, O.OBin{0, k, v, lo, O.OBin{0, hk, hv, hl, hh}}, x) : Maybe<&2, V>}:
  match hl:
    case O.OTip{}:
      rot_lo.single.get(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans, x, k, v, lo, hk, hv,
        O.OTip{}, hh, khk)
    case O.OBin{s, +mk, +mv, +ml, +mh}:
      rot_lo.double.get2(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans, x, k, v, lo, hk, hv,
        mk, mv, ml, mh, hh,
        lt_of(cmp(k, mk), bn.a(~K, ~V, ~cmp, Some{k}, Some{hk}, mk, mv, ml, mh, h_l)),
        lt_of(cmp(mk, hk), bn.b(~K, ~V, ~cmp, Some{k}, Some{hk}, mk, mv, ml, mh, h_l)))

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_lo.double.get2
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rot_lo.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_lo.double