Word.pw_val: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as Word
Lines 331-338 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&start_line=331&end_line=338

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend as A

def pw_val(+n: Nat, +k: Nat, +hk: {Nat.is_lt(k, n) == True{} : Bool}) -> {uw(n, pw(n, k)) == sc(k, 1n) : Nat}:
  match n k:
    case 0n _:
      Empty.absurd({uw(0n, pw(0n, k)) == sc(k, 1n) : Nat}, N.lt_zero_absurd(k, hk))
    case 1n+p 0n:
      Equal.cong(Nat, Nat, z => Nat.add(1n, Nat.double(z)), uw(p, Word.zero(p)), 0n, A.uw_zero(p))
    case 1n+p 1n+j:
      Equal.cong(Nat, Nat, Nat.double, uw(p, pw(p, j)), sc(j, 1n), pw_val(p, j, hk))

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.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=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=uw_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=pw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=uw