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Proof step 176 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) / 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) / 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 177:
# bytes = 1 + # int2bytes(band(b2i(bytes.last), 255) / 256 + bytes2int(bytes.butlast)), 0 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 255 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 0 ≤ band(b2i(bytes.last), 255), 0 ≤ bytes2int(bytes.butlast), ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = [], # bytes = 1, bytes = int2bytes(band(b2i(bytes.last), 255) / 256 + bytes2int(bytes.butlast)) + int2bytes(band(b2i(bytes.last), 255) % 256).last '

Rule argument

Additional information

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