U32Successor.concat_pad: law of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/u32_successor.bend as U32Successor
Lines 95-99 of stelliferous@0.0.2.0/proofs/u32_successor.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/u32_successor.bend&start_line=95&end_line=99

import Base
import stelliferous@0.0.2.0/proofs/natural_addition.bend as Addition
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding
import stelliferous@0.0.2.0/proofs/word_width.bend as WordWidth

law concat_pad:
  for +width: Nat
  for +word: Word(width)
  {WordWidth.transport(Nat.add(width,1n),1n+width,WordEncoding.concat(width,1n,word,Word.zero(1n)),
      Addition.successor_width(width)) == Word.shr.pad(width,word) : Word(1n+width)}

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Nil
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shr.pad
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/natural_addition.bend&name=successor_width
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=concat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_width.bend&name=transport
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_width.bend&name=transport_cons