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Proof step 31 from proof getInt-theorem (previous step)

(band(b2i(by1), 255) i<< 8) + 65536 * band(b2i(by2), 255) < 2 ^ 24 ∧ 0 ≤ 24 ∧ 0 ≤ (band(b2i(by1), 255) i<< 8) + 65536 * band(b2i(by2), 255), 0 ≤ 24 ∧ 24 < 32, band(b2i(by1), 255) i<< 8 < 65536, 0 ≤ band(b2i(by1), 255) i<< 8 ⊦ b2i(by3) * 2 ^ 24 + (band(b2i(by1), 255) i<< 8) + 65536 * band(b2i(by2), 255) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(65536 * band(b2i(by2), 255) + (band(b2i(by1), 255) i<< 8), bor(band(b2i(by0), 255), b2i(by3) * 2 ^ 24)) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), b2i(by3) * 2 ^ 24 + (band(b2i(by1), 255) i<< 8) + 65536 * band(b2i(by2), 255) = bytes2int(by3 ' + by2 ' + by1 ') * 256

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
band(b2i(by1), 255) i<< 8 < 65536, 0 ≤ band(b2i(by1), 255) i<< 8, (band(b2i(by1), 255) i<< 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) i<< 8))) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), 65536 * band(b2i(by2), 255) + (band(b2i(by1), 255) i<< 8) + 16777216 * b2i(by3) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(16777216 * b2i(by3), 65536 * band(b2i(by2), 255) + (band(b2i(by1), 255) i<< 8)) = 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 + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);% ⊦ i + j = j + i;% ⊦ band(i, j) = band(j, i);