BendMlLlama.pick_below: law of bend-ml-llama@0.2.1.0
Import: import bend-ml-llama@0.2.1.0/main.bend as BendMlLlama
Lines 1362-1374 of bend-ml-llama@0.2.1.0/main.bend: https://jend.leeeet.dev/read.txt?path=bend-ml-llama@0.2.1.0/main.bend&start_line=1362&end_line=1374

import Base
import bend-ml-tensor-array@0.1.19.0/main.bend as TA

# PROOF: by induction on cs: the draw returns a candidate of cs, whose id is below n, or id 0 < n when cs is empty.
law pick_below:
  for +cs: List<&2, Cand>
  for +s: Bool
  for +q: Nat
  for +temp: F32
  for +top: F32
  for +target: F32
  for +acc: F32
  for +n: Nat
  for +e: {True{} == below(cs, n) : Bool}
  for pos: {True{} == TA.leb(1n, n) : Bool}
  {True{} == TA.leb(1n+Cand.i(pick.go(cs, s, q, temp, top, target, acc)), n) : Bool}

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=Cand
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=Cand.i
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=and_l
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=and_r
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=below
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=pick.go
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=stops
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=weight
  https://jend.leeeet.dev/definition.txt?path=bend-ml-tensor-array@0.1.19.0/main.bend&name=leb