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

1 < 2 ∧ 0 ≤ 16, 0 < bytes2int(bytes), 2 ^ 16 ≤ bytes2int(bytes), 0 ≤ bytes2int(bytes), # bytes ≤ 2, bytes2int(bytes) < 2 ^ n→i(# bytes * 8 - 1), 0 ≤ 2 ^ n→i(# bytes * 8 - 1) + bytes2int(bytes), 16 < n→i(# bytes * 8 - 1) ⊦ bytes = [], # bytes * 8 - 1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
0 ≤ i ⊦ i < n→i(n) ↔ i→n(i) < n
Proof step 14:
0 ≤ 16, 1 < 2 ∧ 0 ≤ 16, 0 < bytes2int(bytes), 2 ^ 16 ≤ bytes2int(bytes), 0 ≤ bytes2int(bytes), # bytes ≤ 2, bytes2int(bytes) < 2 ^ n→i(# bytes * 8 - 1), 0 ≤ 2 ^ n→i(# bytes * 8 - 1) + bytes2int(bytes), i→n(16) < # bytes * 8 - 1 ⊦ bytes = [], # bytes * 8 - 1 = 0

Rule argument

seq: 0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n subst: [n, i] → [# bytes * 8 - 1, 16] rotate: F spec: intnat inst: name: num-n2i-ls-02

Additional information

Used terms: # bytes * 8 - 1, 16