Arith.mul_pow: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as Arith
Lines 187-194 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&start_line=187&end_line=194

import Base

# (x y)^k == x^k y^k   (Mathlib mul_pow)
def mul_pow(+x: Nat, +y: Nat, +k: Nat) -> {Nat.pow(Nat.mul(x, y), k) == Nat.mul(Nat.pow(x, k), Nat.pow(y, k)) : Nat}:
  match k:
    case 0n:
      {==}
    case 1n+ +kp:
      %Equal.sym(Nat, Nat.pow(Nat.mul(x, y), kp), Nat.mul(Nat.pow(x, kp), Nat.pow(y, kp)), mul_pow(x, y, kp)) : {Nat.mul(Nat.mul(x, y), _) == Nat.mul(Nat.mul(x, Nat.pow(x, kp)), Nat.mul(y, Nat.pow(y, kp))) : Nat}
      mul_swap4(x, y, Nat.pow(x, kp), Nat.pow(y, kp))

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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/math/natural/arith.bend&name=mul_swap4