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Proof step 15 from proof bytes2int-size-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;