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Proof step 16 from proof bytes2int-size-03 (previous step)

2 ^ (n→i(# bytes1) * 8) ≤ bytes2int(by ' + bytes1), 0 < b2i(by), band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes1) < 256 * 2 ^ (8 * n→i(# bytes1)), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → bytes2int(by ' + bytes0) < 2 ^ (n→i(# bytes0) * 8) ∧ 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(by ' + bytes1), band(255, b2i(by0)), 2 ^ (8 * n→i(# bytes1))] 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;% ⊦ i * j = j * i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ (* i2) * i + j < (* i1) * i ↔ j < (i1 - i2) * i;% ⊦ i * 0 = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 256, bytes2int(by ' + bytes1), band(255, b2i(by0)), 2 ^ (8 * n→i(# bytes1))