ProofBase.append_inj_l: law of lawful-arrays@0.1.0.0
Import: import lawful-arrays@0.1.0.0/proof_base.bend as ProofBase
Lines 472-481 of lawful-arrays@0.1.0.0/proof_base.bend: https://jend.leeeet.dev/read.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&start_line=472&end_line=481

import Base

# Two appends with equally long first parts: the first parts are equal...
law append_inj_l:
  for -A: Data
  for +x1: List<&2, A>
  for +x2: List<&2, A>
  for -y1: List<&2, A>
  for -y2: List<&2, A>
  for hl: {List.length(&2, A, x1) == List.length(&2, A, x2) : Nat}
  for +e: {List.append(&2, A, x1, y1) == List.append(&2, A, x2, y2) : List<&2, A>}
  {x1 == x2 : List<&2, A>}

Uses (10):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=cons_inj_h
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=cons_inj_t
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=succ_inj
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=succ_ne_zero