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Proof step 9 from proof bytes2int-first-pos (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 10:
0 ≤ bytes2int(by ' + bytes.butlast), 0 ≤ b2i(by), band(255, b2i(bytes.last)) + 256 * bytes2int(by ' + bytes.butlast) < 0, ∀ by, bytes0. # bytes0 < # bytes → bytes2int(by ' + bytes0) < 0 ∧ 0 ≤ b2i(by) → false ⊦ bytes2int(by ' + bytes.butlast) = 0, bytes = []

Rule argument

fma: bytes2int(by ' + bytes.butlast) = 0

Additional information

Used simplifier rules: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i); Used formulas: bytes2int(by ' + bytes.butlast) = 0