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Proof step 17 from proof bytes2int-size-02 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

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

Additional information

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