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Proof step 179 from proof bytes2int-int2bytes-len-eq (previous step)

0 < 256 ∧ 0 ≤ band(b2i(bytes.last), 255) ∧ band(b2i(bytes.last), 255) < 256, # bytes = 1 + # int2bytes(0 + 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(0 + bytes2int(bytes.butlast)) + int2bytes(band(b2i(bytes.last), 255) % 256).last '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 180:
# bytes = 1 + # int2bytes(bytes2int(bytes.butlast)), band(b2i(bytes.last), 255) < 256, 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(bytes2int(bytes.butlast)) + int2bytes(band(b2i(bytes.last), 255)).last '

Rule argument

Additional information

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