ProofShift.take_snoc: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_shift.bend as ProofShift
Lines 70-75 of lawful-bytes@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&start_line=70&end_line=75

import Base

law take_snoc:
  for +ys: List<&2, U32>
  for +j: Nat
  for +x: U32
  for +h: {List.get(&2, U32, ys, j) == Some{x} : Maybe<&2, U32>}
  {List.take(&2, U32, ys, Nat.add(j, 1n)) == List.append(&2, U32, List.take(&2, U32, ys, j), [x]) : List<&2, U32>}

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=none_some
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=some_inj
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_seq.bend&name=take_zero