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Proof step 28 from proof int2bytes-len-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1))
Proof step 30:
0 < j, 0 < j, ¬ j < 2 ^ (n→i(i→n(8 * i) + 1) - 1), 8 * i + 1 < 8 * (i + 1), j < 2 ^ (8 * (i + 1) - 1), 0 ≤ i ⊦ # int2bits(j) / 8 = i→n(i), # int2bits(j) % 8 = 0

Rule argument

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

Additional information

Used terms: j, i→n(8 * i) + 1