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Proof step 310 from proof int2bytes-rec-pos-any (previous step)

8 - # int2bits(j % 2 ^ (i * 8)) ≠ 0, i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 ≤ b2i(i2b(j % 2 ^ (i * 8))) ⊦ i = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(false, 8 * (i→n(i) - 1)) + mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - 1 = 0, mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i2b(bits2int(false ' + int2bits(j % 2 ^ (i * 8)))) = i2b(j % 2 ^ (i * 8)), bits2int(false ' + int2bits(j % 2 ^ (i * 8))) = j % 2 ^ (i * 8)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 311:
i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 ≤ b2i(i2b(j % 2 ^ (i * 8))) ⊦ i = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(false, 8 * (i→n(i) - 1)) + mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - 1 = 0, mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i2b(bits2uint(int2bits(j % 2 ^ (i * 8)))) = i2b(j % 2 ^ (i * 8)), bits2uint(int2bits(j % 2 ^ (i * 8))) = j % 2 ^ (i * 8)

Rule argument

Additional information

Used simplifier rules: ⊦ i2b(i) ≠ i2b(j) → i ≠ j; (forward)% ⊦ n < m → m - n ≠ 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits2int(false ' + bits) = bits2uint(bits);% ⊦ i * j = j * i;