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Proof step 15 from proof bytes2int-size-06 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
0 < 255 * (2 ^ (8 * n→i(# bytes1)) + bytes2int(by ' + bytes1)) + band(255, b2i(by0)), 0 ≤ 256 * (bytes2int(by ' + bytes1) + 2 ^ (8 * n→i(# bytes1))) + band(255, b2i(by0)), b2i(by) < 0, bytes2int(by ' + bytes1) + 2 ^ (8 * n→i(# bytes1)) < 0, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → 0 ≤ bytes2int(by ' + bytes0) + 2 ^ (8 * n→i(# bytes0)) ∧ b2i(by) < 0 → b2i(by) = ~1 ⊦ b2i(by) = ~1

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ j < (* i1) * j + i ↔ 0 < (i1 - 1) * j + i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j + i * j0 = i * (j + j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ n→i(n);% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i * j = j * i;