ProofSeq.take_set_succ: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_seq.bend as ProofSeq
Lines 82-88 of lawful-bytes@0.1.1.0/proof_seq.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_seq.bend&start_line=82&end_line=88

import Base

# Setting index n and keeping n + 1 elements: the first n, then v.
law take_set_succ:
  for +xs: List<&2, U32>
  for +n: Nat
  for +v: U32
  for +h: {Nat.is_lt(n, List.length(&2, U32, xs)) == True{} : Bool}
  {List.take(&2, U32, List.set(&2, U32, xs, n, v), Nat.add(n, 1n)) == List.append(&2, U32, List.take(&2, U32, xs, n), [v]) : List<&2, U32>}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.set
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  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=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_seq.bend&name=take_zero