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Proof step 173 from proof bytes2int-int2bytes-len-eq (previous step)

¬((bytes2int(bytes.butlast) * 256) % 256 = 0 ∧ 0 ≤ bytes2int(bytes.butlast) * 256 ∧ 0 ≤ band(b2i(bytes.last), 255) ∧ 0 < 256), # bytes = # int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) / 256) + 1, 0 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 255 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = [], # bytes = 1, bytes = int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) / 256) + int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) % 256).last '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 174:
# bytes = # int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) / 256) + 1, 0 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 255 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), bytes2int(bytes.butlast) < 0, ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = [], # bytes = 1, bytes = int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) / 256) + int2bytes((bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)) % 256).last '

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ band(i, j) = band(j, i);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0;