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Proof step 18 from proof bytes2int-size-05 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [256, bytes2int(i2b(~1) ' + by ' + bytes1) + 2 ^ (8 * (1 + n→i(# bytes1))), band(255, b2i(by0)), 0] rotate: F spec: int-mult inst: name: modlsp-02

Additional information

Used simplifier rules: ⊦ ¬ 256 ≤ band(i, 255);% ⊦ abs(band(255, b2i(by))) = band(255, b2i(by));% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i + 0 = i;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i); Used terms: 256, bytes2int(i2b(~1) ' + by ' + bytes1) + 2 ^ (8 * (1 + n→i(# bytes1))), band(255, b2i(by0)), 0