ProofCut.ends_push: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_cut.bend as ProofCut
Lines 468-474 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=468&end_line=474

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

# Pushing a byte onto the first piece shifts every end by one.
law ends_push:
  for +x: U32
  for +ps: List<&2, List<&2, U32>>
  for +s: Nat
  for +hnn: {nn(ps) == True{} : Bool}
  {F.ends(F.split.push(x, ps), s) == F.ends(ps, Nat.add(s, 1n)) : List<&2, Nat>}

Uses (13):
  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.length
  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-arrays@0.1.0.0/proof_base.bend&name=false_ne_true
  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.push
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=nn
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_assoc