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Proof step 88 from proof int2bytes-len-ls-01 (previous step)

# int2bits(i) = i→n(i0) * 8 + 1, # int2bits(i) / 8 = i→n(i0), 0 < i, i→n(i0) * 8 < # int2bits(i), i0 < n→i(n), 2 ^ (n→i(n) * 8 - 1) ≤ i, 0 < i0 ⊦ n = 1, n = 0, i0 = 0, i = 0, # int2bits(i) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 89:
⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1))
Proof step 90:
0 < i, # int2bits(i) = i→n(i0) * 8 + 1, # int2bits(i) / 8 = i→n(i0), 0 < i, ¬ i < 2 ^ (n→i(i→n(i0) * 8) - 1), i0 < n→i(n), 2 ^ (n→i(n) * 8 - 1) ≤ i, 0 < i0 ⊦ n = 1, n = 0, i0 = 0, i = 0, # int2bits(i) % 8 = 0

Rule argument

seq: ⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1)) subst: [i, m] → [i, i→n(i0) * 8] rotate: F spec: int2bits inst: name: int2bits-lslen-06

Additional information

Used terms: i, i→n(i0) * 8