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Proof step 149 from proof bytes2int-int2bytes-len-eq (previous step)

0 ≤ 256 * b2i(by0) + band(b2i(by), 255), b2i(by0) < 0, ~129 < i, i < 0, ∀ bytes0. # bytes0 < #((by0 + []) + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = i2b(0), by0 ' + by ' = i2b(0) ' + i2b(i) '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 150:
⊦ i * j = j * i
Proof step 151:
0 ≤ b2i(by0) * 256 + band(b2i(by), 255), b2i(by0) < 0, ~129 < i, i < 0, ∀ bytes0. # bytes0 < #((by0 + []) + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by = i2b(0), by0 ' + by ' = i2b(0) ' + i2b(i) '

Rule argument

seq: ⊦ i * j = j * i subst: [j, i] → [b2i(by0), 256] rotate: F spec: int-mult inst: name: commutativity

Additional information

Used terms: b2i(by0), 256