U32.pow2_pow: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U32
Lines 32-38 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&start_line=32&end_line=38

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

def pow2_pow(+k: Nat) -> {SC.pow2(k) == Nat.pow(2n, k) : Nat}:
  match k:
    case 0n:
      {==}
    case 1n+p:
      %pow2_pow(p) : {Nat.double(SC.pow2(p)) == Nat.add(_, Nat.add(_, 0n)) : Nat}
      double_pow(SC.pow2(p))

Uses (6):
  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.pow
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=double_pow
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2