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Proof step 49 from proof int2bytes-len-neg-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ j < 0 ∧ 1 < n → (# int2bits(j) = n ↔ ~(2 ^ (n→i(n) - 1)) ≤ j ∧ j < ~(2 ^ (n→i(n) - 2)))
Proof step 51:
¬(j < 0 ∧ 1 < m * 8 + n), # int2bits(j) = m * 8 + n, 0 ≤ i, m * 8 + n ≤ i→n(8 * (i + 1)) + 1, j + 2 ^ (8 * (i + 1) - 1) < 0, j < 0, n < 8 ⊦ n = 0, m + 1 = i→n(i + 2), j + 2 ^ (8 * (i + 1)) = 0
Proof step 54:
j < 0 ∧ 1 < m * 8 + n, ~(2 ^ (n→i(m * 8 + n) - 1)) ≤ j ∧ j < ~(2 ^ (n→i(m * 8 + n) - 2)), 0 ≤ i, m * 8 + n ≤ i→n(8 * (i + 1)) + 1, j + 2 ^ (8 * (i + 1) - 1) < 0, j < 0, n < 8 ⊦ n = 0, m + 1 = i→n(i + 2), j + 2 ^ (8 * (i + 1)) = 0

Rule argument

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

Additional information

Used terms: m * 8 + n, j