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Proof step 10 from proof bytes2int-int2bytes-len-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
255 < i ⊦ int2bytes(i) = int2bytes(i / 256) + int2bytes(i % 256).last '
Proof step 12:
¬ 255 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), # bytes = # int2bytes(bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)), ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = int2bytes(bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)), # bytes = 1, bytes = []
Proof step 170:
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 = []

Rule argument

name: int2bytes-rec-pos rotate: F subst: [i] → [bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)]

Additional information

Used terms: bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)