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Proof step 19 from proof bytes2int-size-01 (previous step)

2 ^ ((n→i(# bytes1) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes1), b2i(by) < 0, 256 * bytes2int(i2b(0) ' + by ' + bytes1) + band(255, b2i(by0)) < 2 ^ (8 * (1 + n→i(# bytes1)) - 1) * 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → b2i(by) < 0 → 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes0) ⊦ 256 * bytes2int(i2b(0) ' + by ' + bytes1) + band(255, b2i(by0)) < 256 * 2 ^ (8 * (1 + n→i(# bytes1)) - 1) ∧ abs(band(255, b2i(by0))) < 256

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ 256 ≤ band(i, 255);% ⊦ band(i, j) = band(j, i);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ abs(band(255, b2i(by))) = band(255, b2i(by));% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;