PROOF.un.pad: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 788-797 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=788&end_line=797

import Base

def un.pad(p: Nat, t: Word(p)) -> {Word.to_nat(1n+p, Word.shr.pad(p, t)) == Word.to_nat(p, t) : Nat}:
  match p:
    case 0n:
      {==}
    case 1n+ +q:
      match t:
        case WCon{False{}, +r}:
          un.double_cong(Word.to_nat(1n+q, Word.shr.pad(q, r)), Word.to_nat(q, r), un.pad(q, r))
        case WCon{True{}, +r}:
          un.succ_cong(Nat.double(Word.to_nat(1n+q, Word.shr.pad(q, r))), Nat.double(Word.to_nat(q, r)), un.double_cong(Word.to_nat(1n+q, Word.shr.pad(q, r)), Word.to_nat(q, r), un.pad(q, r)))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  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.shr.pad
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.double_cong
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.succ_cong