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Proof step 28 from proof int2bytes-len-ls-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ 0 ≤ j ∧ 1 < n → (# int2bits(j) = n ↔ 2 ^ (n→i(n) - 2) ≤ j ∧ j < 2 ^ (n→i(n) - 1))
Proof step 30:
¬(0 ≤ i ∧ 1 < 1 + 8 * i→n(i0)), # int2bits(i) / 8 = i→n(i0), # int2bits(i) = 1 + 8 * i→n(i0), 0 < i, 0 ≤ i0 ⊦ # int2bits(i) % 8 = 0, i = 0, n ≤ i→n(i0) ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1)
Proof step 33:
0 ≤ i ∧ 1 < 1 + 8 * i→n(i0), # int2bits(i) / 8 = i→n(i0), 2 ^ (n→i(1 + 8 * i→n(i0)) - 2) ≤ i ∧ i < 2 ^ (n→i(1 + 8 * i→n(i0)) - 1), 0 < i, 0 ≤ i0 ⊦ # int2bits(i) % 8 = 0, i = 0, n ≤ i→n(i0) ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1)

Rule argument

seq: ⊦ 0 ≤ j ∧ 1 < n → ( # int2bits(j) = n ↔ 2 ^ (n→i(n) - 2) ≤ j ∧ j < 2 ^ (n→i(n) - 1)) subst: [n, j] → [1 + 8 * i→n(i0), i] rotate: F spec: int2bits inst: name: int2bits-leneq-pos

Additional information

Used terms: 1 + 8 * i→n(i0), i