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Proof step 12 from proof bytes2int-size-05 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
0 ≤ b2i(by), band(255, b2i(by0)) + 256 * bytes2int(i2b(~1) ' + by ' + bytes1) + 2 ^ (8 * (2 + n→i(# bytes1))) < 0, 0 ≤ 2 ^ ((n→i(# bytes1) + 1) * 8) + bytes2int(i2b(~1) ' + by ' + bytes1), 255 * bytes2int(i2b(~1) ' + by ' + bytes1) + band(255, b2i(by0)) + 2 ^ (8 * (2 + n→i(# bytes1))) < 2 ^ ((n→i(# bytes1) + 1) * 8), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → 2 ^ ((n→i(# bytes0) + 1) * 8) + bytes2int(i2b(~1) ' + by ' + bytes0) < 0 ∧ 0 ≤ b2i(by) → false ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* i2) * i + j < i + j0 ↔ (i2 - 1) * i + j < j0;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;