ProofCut.pb: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_cut.bend as ProofCut
Lines 557-564 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=557&end_line=564

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

# The ends of split(ys) from s give back its pieces when ys starts xs at s.
law pb:
  for +ys: List<&2, U32>
  for +xs: List<&2, U32>
  for +s: Nat
  for +sep: U32
  for +hp: {List.take(&2, U32, List.drop(&2, U32, xs, s), List.length(&2, U32, ys)) == ys : List<&2, U32>}
  {PN(F.ends(F.split(ys, sep), s), xs, s) == F.split(ys, sep) : List<&2, List<&2, U32>>}

Uses (20):
  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.drop
  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.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.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/proof_cut.bend&name=PN
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=pbc
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=pre_get
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=pre_tail
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_zero