U32.pad_value: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U32
Lines 125-134 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&start_line=125&end_line=134

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

def pad_value(+n: Nat, +w: Word(n)) -> {S.unsigned(1n+n, Word.shr.pad(n, w)) == S.unsigned(n, w) : Nat}:
  match n:
    case 0n:
      match w:
        case WNil{}:
          {==}
    case 1n+p:
      match w:
        case WCon{b, t}:
          Equal.cong(Nat, Nat, v => Nat.add(S.bit_value(b), Nat.double(v)), S.unsigned(1n+p, Word.shr.pad(p, t)), S.unsigned(p, t), pad_value(p, t))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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.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.Nil
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shr.pad
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=bit_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned