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Proof step 165 from proof bytes2int-int2bytes-len-eq (previous step)

b2i(by0) = i + 1, i * 256 + band(b2i(by), 255) < 0, ~129 < i * 256 + band(b2i(by), 255), ~1 ≤ i, 255 * i + band(b2i(by), 255) ≤ 0, i ≤ 0, ∀ bytes0. # bytes0 < #((by0 + []) + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = i2b(0), by0 = i2b(0)

User applied rule cut formula

And closed the goal!

Rule argument

fma: i = ~1

Additional information

Used simplifier rules: ⊦ b2i(by) = i → (i2b(i) ≠ by ↔ false);% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = 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: i = ~1