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Proof step 170 from proof bytes2int-int2bytes-len-eq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 171:
# 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 '

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ # by ' = 0 +1;% ⊦ #(bytes + bytes0) = # bytes + # bytes0;