ProofNat.pow_sub1: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_nat.bend as ProofNat
Lines 1409-1412 of lawful-words@0.1.0.0/proof_nat.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_nat.bend&start_line=1409&end_line=1412

import Base

# 2^(1+j) - 1 = 1 + 2 (2^j - 1).
law pow_sub1:
  for +j: Nat
  {Nat.sub(Nat.pow(2n, 1n+j), 1n) == 1n+Nat.double(Nat.sub(Nat.pow(2n, j), 1n)) : Nat}

Uses (9):
  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.double
  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=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul2
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=pow_one_plus
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=pow_sub1.go