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Proof step 12 from proof band-65535-neg (previous step)

0 ≤ 2 ^ n→i(# bytes * 8 - 1) + bytes2int(bytes), # bytes ≤ 2, bytes2int(bytes) < 0, bytes2int(bytes) ≤ ~65537, bytes2int(bytes) < 2 ^ n→i(# bytes * 8 - 1) ⊦ 0 ≤ 2 ^ n→i(2 * 8 - 1) + bytes2int(bytes), bytes = [], (bytes2int(bytes) + 1) % 65536 = 1 + bytes2int(bytes)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ m * n = n * m
Proof step 14:
0 ≤ 2 ^ n→i(# bytes * 8 - 1) + bytes2int(bytes), # bytes ≤ 2, bytes2int(bytes) < 0, bytes2int(bytes) ≤ ~65537, bytes2int(bytes) < 2 ^ n→i(# bytes * 8 - 1) ⊦ 0 ≤ 2 ^ n→i(8 * 2 - 1) + bytes2int(bytes), bytes = [], (bytes2int(bytes) + 1) % 65536 = 1 + bytes2int(bytes)

Rule argument

seq: ⊦ m * n = n * m subst: [n, m] → [8, 2] rotate: F spec: nat-mult inst: name: mult-c

Additional information

Used terms: 8, 2