ProofCut.pbc: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_cut.bend as ProofCut
Lines 526-536 of lawful-fields@0.1.1.0/proof_cut.bend: https://jend.leeeet.dev/read.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&start_line=526&end_line=536

import Base
import lawful-fields@0.1.1.0/defs.bend as F

law pbc:
  for +x: U32
  for +t: List<&2, U32>
  for +xs: List<&2, U32>
  for +s: Nat
  for +sep: U32
  for +b: Bool
  for +hb: {U32.is_eq(x, sep) == b : Bool}
  for +hg: {List.get(&2, U32, xs, s) == Some{x} : Maybe<&2, U32>}
  for +ih: {PN(F.ends(F.split(t, sep), Nat.add(s, 1n)), xs, Nat.add(s, 1n)) == F.split(t, sep) : List<&2, List<&2, U32>>}
  {PN(F.ends(F.split(x <> t, sep), s), xs, s) == F.split(x <> t, sep) : List<&2, List<&2, U32>>}

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=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.get
  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=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=slice
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=slice_zero
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=sub_self
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/defs.bend&name=ends
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/defs.bend&name=split
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/defs.bend&name=split.fin
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=PN
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=pb_push
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=split_nn
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_zero