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Proof step 240 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 241:
⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0
Proof step 242:
i→n(i) - 1 = 0 ∨ 8 = 0, 0 < i, # int2bits(j % 2 ^ (i * 8)) < 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(int2bits(j % 2 ^ (i * 8))), i = 0

Rule argument

seq: ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0 subst: [m, m0] → [8, i→n(i) - 1] rotate: F spec: nat-mult inst: name: zero-01

Additional information

Used terms: 8, i→n(i) - 1