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Proof step 7 from proof bytes2int-size-05 (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 8:
band(255, b2i((by ' + bytes).last)) + 256 * bytes2int(i2b(~1) ' + (by ' + bytes).butlast) + 2 ^ ((n→i(# bytes) + 1) * 8) < 0, 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < # bytes → 2 ^ ((n→i(# bytes0) + 1) * 8) + bytes2int(i2b(~1) ' + by ' + bytes0) < 0 ∧ 0 ≤ b2i(by) → false ⊦ bytes = []

Rule argument

fma: bytes = []

Additional information

Used simplifier rules: bytes2int-one: ⊦ bytes2int(by ') = b2i(by);% ⊦ # [] = 0;% ⊦ bytes + [] = bytes;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ by '.butlast = [];%~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i;% ⊦ by '.last = by;% ⊦ 0 ≤ i → band(i, 255) = i % 256;% ⊦ b2i(by) % 256 = b2i(by);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used formulas: bytes = []