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Proof step 299 from proof int2bytes-rec-pos-any (previous step)

m * 8 = 0, i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), m < i→n(i), # int2bits(j % 2 ^ (i * 8)) < 8, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i = 0, bits2bytes(mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(int2bits(j % 2 ^ (i * 8))), mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - m + 1 = 0, mklist(false, 8 * (i→n(i) - m + 1)) + mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 300:
⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0
Proof step 301:
m = 0 ∨ 8 = 0, i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), m < i→n(i), # int2bits(j % 2 ^ (i * 8)) < 8, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i = 0, bits2bytes(mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(int2bits(j % 2 ^ (i * 8))), mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - m + 1 = 0, mklist(false, 8 * (i→n(i) - m + 1)) + mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = []

Rule argument

seq: ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0 subst: [m, m0] → [8, m] rotate: F spec: nat-mult inst: name: zero-01

Additional information

Used terms: 8, m