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Proof step 6 from proof bytes2int-size-01 (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
b2i(by) < 0, band(255, b2i((by ' + bytes).last)) + 256 * bytes2int(i2b(0) ' + (by ' + bytes).butlast) < 2 ^ ((n→i(# bytes) + 1) * 8 - 1), ∀ by, bytes0. # bytes0 < # bytes → true → b2i(by) < 0 → 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes0) ⊦ bytes = []

Rule argument

fma: bytes = []

Additional information

Used simplifier rules: bytes2int-zero: ⊦ bytes2int(i2b(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);% ⊦ # [] = 0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ ¬ b2i(by) < ~128; Used formulas: bytes = []