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Proof step 34 from proof getInt-theorem (previous step)

0 ≤ 8 ∧ 8 < 32, band(b2i(by1), 255) * 2 ^ 8 < 65536, 0 ≤ band(b2i(by1), 255) * 2 ^ 8, band(b2i(by1), 255) * 2 ^ 8 + 65536 * band(b2i(by2), 255) < 16777216, 0 ≤ band(b2i(by2), 255) ⊦ bor(16777216 * b2i(by3), bor(band(b2i(by0), 255), 65536 * band(b2i(by2), 255) + band(b2i(by1), 255) * 2 ^ 8)) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), 65536 * band(b2i(by2), 255) + band(b2i(by1), 255) * 2 ^ 8 + 16777216 * b2i(by3) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(16777216 * b2i(by3), 65536 * band(b2i(by2), 255) + band(b2i(by1), 255) * 2 ^ 8) = bytes2int(by3 ' + by2 ' + by1 ') * 256

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
0 ≤ band(b2i(by2), 255), band(b2i(by1), 255) < 256, 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255) < 16777216, 0 ≤ band(b2i(by1), 255) ⊦ bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), bor(band(b2i(by0), 255), 16777216 * b2i(by3))) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), 16777216 * b2i(by3) + 256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), 16777216 * b2i(by3)) = bytes2int(by3 ' + by2 ' + by1 ') * 256

Rule argument

Additional information

Used simplifier rules: ⊦ bor(i, j) = bor(j, i);% ⊦ bor(bor(i, i0), j0) = bor(i, bor(i0, j0));% ⊦ bor(i, j) ≠ bor(i0, j) → i ≠ i0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i + j = j + i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i);% ⊦ band(i, j) = band(j, i);