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Proof step 33 from proof int2bytes-len-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ 0 ≤ j ∧ 1 < n → (# int2bits(j) = n ↔ 2 ^ (n→i(n) - 2) ≤ j ∧ j < 2 ^ (n→i(n) - 1))
Proof step 35:
¬(0 ≤ j ∧ 1 < m * 8 + n), # int2bits(j) = m * 8 + n, 2 ^ (8 * i) ≤ j, 0 ≤ i, j < 2 ^ (8 * (i + 1) - 1), 8 * i + 1 < 8 * (i + 1), 0 < j, n < 8 ⊦ n = 0, m = i→n(i)
Proof step 38:
0 ≤ j ∧ 1 < m * 8 + n, 2 ^ (n→i(m * 8 + n) - 2) ≤ j ∧ j < 2 ^ (n→i(m * 8 + n) - 1), 2 ^ (8 * i) ≤ j, 0 ≤ i, j < 2 ^ (8 * (i + 1) - 1), 8 * i + 1 < 8 * (i + 1), 0 < j, n < 8 ⊦ n = 0, m = i→n(i)

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] → [m * 8 + n, j] rotate: F spec: int2bits inst: name: int2bits-leneq-pos

Additional information

Used terms: m * 8 + n, j