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Proof step 12 from proof bytes2int-first-pos (previous step)

0 ≤ b2i(by), band(255, b2i(bytes.last)) + 256 * bytes2int(by ' + bytes.butlast) < 0, 0 < bytes2int(by ' + bytes.butlast), ∀ by, bytes0. # bytes0 < # bytes → bytes2int(by ' + bytes0) < 0 ∧ 0 ≤ b2i(by) → false ⊦ band(255, b2i(bytes.last)) < 0, bytes2int(by ' + bytes.butlast) = 0, bytes = []

User applied rule cut formula

And obtained the following new goals

Proof step 13:
band(255, b2i(bytes.last)) < 128, 0 ≤ b2i(by), band(255, b2i(bytes.last)) + 256 * bytes2int(by ' + bytes.butlast) < 0, 0 < bytes2int(by ' + bytes.butlast), ∀ by, bytes0. # bytes0 < # bytes → bytes2int(by ' + bytes0) < 0 ∧ 0 ≤ b2i(by) → false ⊦ band(255, b2i(bytes.last)) < 0, bytes2int(by ' + bytes.butlast) = 0, bytes = []

Rule argument

fma: band(255, b2i(bytes.last)) < 128

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i + j < j ↔ i < 0;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used formulas: band(255, b2i(bytes.last)) < 128