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Proof step 28 from proof getInt-theorem (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255) < 65536 * band(b2i(by2), 255) + 256 * 256

Additional information

Used simplifier rules: ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ band(i, j) = band(j, i);% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);% ⊦ 0 ≤ i ∧ i ≤ i0 → ¬ i0 < band(i, j);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j); Used formulas: 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255) < 65536 * band(b2i(by2), 255) + 256 * 256