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Proof step 145 from proof int2bytes-rec-pos-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 146:
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) ⊦ bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + 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

Rule argument

Additional information

Used simplifier rules: ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ m ≠ n → (m ≤ n ↔ m < n);% ⊦ i * j = j * i;