BendMlLlama.ins_below: law of bend-ml-llama@0.2.1.0
Import: import bend-ml-llama@0.2.1.0/main.bend as BendMlLlama
Lines 1293-1303 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=1293&end_line=1303

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

# PROOF: by induction on cs. Inserting puts the new candidate (id i < n) at the front, or keeps the head and
# inserts into the tail, whose ids are below n by the induction hypothesis.
law ins_below:
  for +cs: List<&2, Cand>
  for +g: Bool
  for +v: F32
  for +i: Nat
  for +n: Nat
  for +e: {True{} == below(cs, n) : Bool}
  for ei: {True{} == TA.leb(1n+i, n) : Bool}
  {True{} == below(ins(cs, g, v, i), n) : Bool}

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  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=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=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=goes_before
  https://jend.leeeet.dev/definition.txt?path=bend-ml-llama@0.2.1.0/main.bend&name=ins
  https://jend.leeeet.dev/definition.txt?path=bend-ml-tensor-array@0.1.19.0/main.bend&name=leb