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Proof step 119 from proof bxor-flip-one-bit (previous step)

# bits = i→n(j), bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))) = (false ' + true ') + bitsxor(bits, mklist(false, i→n(j))), int2bits(i) = false ' + bits, 0 ≤ j, false ∈ int2bits(i), 2 ^ j * 2 < i, 0 < i ⊦ bits = [], # int2bits(i) = 2 + i→n(j), i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 120:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j
Proof step 121:
0 ≤ j, # bits = i→n(j), bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))) = (false ' + true ') + bitsxor(bits, mklist(false, i→n(j))), int2bits(i) = false ' + bits, 0 ≤ j, false ∈ int2bits(i), 2 ^ (j + 1) < i, 0 < i ⊦ bits = [], # int2bits(i) = 2 + i→n(j), i = 0

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [j, 2] rotate: T spec: int-pot inst: name: succ

Additional information

Used terms: j, 2