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

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: bytes = []

Additional information

Used simplifier rules: bytes2int-zero: ⊦ bytes2int(i2b(0) ') = 0;% ⊦ # [] = 0;% ⊦ bytes + [] = bytes;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ by '.butlast = [];% ⊦ by '.last = by;% ⊦ i < 0 → band(i, 255) = (i + 1) % 256 + 255;% ⊦ (b2i(by) + 1) % 256 = b2i(by) + 1;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used formulas: bytes = []