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Proof step 21 from proof bytes2int-int2bytes-len-eq (previous step)

# bytes1 + 1 = # int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255)), bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~128, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 = [], bytes1 + by ' = int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ~256 < i ∧ i < ~128 → int2bytes(i) = i2b(~1) ' + i2b(i) '
Proof step 23:
¬(~256 < bytes2int(bytes1) * 256 + band(b2i(by), 255) ∧ bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~128), # bytes1 + 1 = # int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255)), bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~128, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 = [], bytes1 + by ' = int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255))
Proof step 114:
~256 < bytes2int(bytes1) * 256 + band(b2i(by), 255) ∧ bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~128, # bytes1 + 1 = #(i2b(~1) ' + i2b(bytes2int(bytes1) * 256 + band(b2i(by), 255)) '), bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~128, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 = [], bytes1 + by ' = i2b(~1) ' + i2b(bytes2int(bytes1) * 256 + band(b2i(by), 255)) '

Rule argument

name: int2bytes-byte-neg rotate: F subst: [i] → [bytes2int(bytes1) * 256 + band(b2i(by), 255)]

Additional information

Used terms: bytes2int(bytes1) * 256 + band(b2i(by), 255)