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Proof step 15 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) ≤ 255, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 + by ' = int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255)), bytes1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
127 < i, i ≤ 255 ⊦ int2bytes(i) = i2b(0) ' + i2b(i - 256) '
Proof step 17:
¬(127 < bytes2int(bytes1) * 256 + band(b2i(by), 255) ∧ bytes2int(bytes1) * 256 + band(b2i(by), 255) ≤ 255), # bytes1 + 1 = # int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255)), bytes2int(bytes1) * 256 + band(b2i(by), 255) ≤ 255, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 + by ' = int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255)), bytes1 = []
Proof step 133:
127 < bytes2int(bytes1) * 256 + band(b2i(by), 255) ∧ bytes2int(bytes1) * 256 + band(b2i(by), 255) ≤ 255, # bytes1 + 1 = #(i2b(0) ' + i2b(bytes2int(bytes1) * 256 + band(b2i(by), 255) - 256) '), bytes2int(bytes1) * 256 + band(b2i(by), 255) ≤ 255, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 + by ' = i2b(0) ' + i2b(bytes2int(bytes1) * 256 + band(b2i(by), 255) - 256) ', bytes1 = []

Rule argument

name: int2bytes-le255 rotate: F subst: [i] → [bytes2int(bytes1) * 256 + band(b2i(by), 255)]

Additional information

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