PROOF.rot_lo.get: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 729-745 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=729&end_line=745

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.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),
  hi: O.OMap<K, V>, +ub: Maybe<&2, K>, +x: K, +k: K, +v: V, +lo: O.OMap<K, V>,
  +eh: {Laws.bounded(~K, ~V, ~cmp, hi, Some{k}, ub) == True{} : Bool}
) -> {g(~K, ~V, ~cmp, O.OMap.rot_lo(K, V, k, v, lo, hi), x)
      == g(~K, ~V, ~cmp, O.OBin{0, k, v, lo, hi}, x) : Maybe<&2, V>}:
  match hi:
    case O.OTip{}:
      {==}
    case O.OBin{s, +hk, +hv, +hl, +hh}:
      rot_lo.pick.get(~K, ~V, ~cmp, ~refl, ~eq, ~flip, ~trans,
        U32.is_lt((O.OMap.size(K, V, hl) + 1 : U32),
          (2 * (O.OMap.size(K, V, hh) + 1) : U32)),
        x, k, v, lo, hk, hv, hl, hh,
        lt_of(cmp(k, hk), bn.a(~K, ~V, ~cmp, Some{k}, ub, hk, hv, hl, hh, eh)),
        bn.l(~K, ~V, ~cmp, Some{k}, ub, hk, hv, hl, hh, eh))

Uses (20):
  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=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mul
  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.l
  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.pick.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
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/omap.bend&name=OMap.size