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Proof step 7 from proof bytes2int-size-07 (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: bytes = []

Additional information

Used simplifier rules: bytes2int-one: ⊦ bytes2int(by ') = b2i(by);% ⊦ 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);% ⊦ # [] = 0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;%i ≥ 128 ⊦ ¬ (* i) ≤ b2i(by); Used formulas: bytes = []