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Proof step 58 from proof int2bytes-len-neg-01 (previous step)

0 ≤ i, 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 2 ^ (n→i(m) * 8 + n→i(n) - 1), j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, 8 * (i + 1) < n→i(m) * 8 + n→i(n), n < 8, j < 0, j + 2 ^ (8 * (i + 1) - 1) < 0, m * 8 + n ≤ 9 + 8 * i→n(i) ⊦ m * 8 + n = 0, j + 2 ^ (8 * (i + 1)) = 0, m + 1 = i→n(i + 2), n = 0, m = 0 ∧ n = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 59:
⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0)
Proof step 60:
¬ 0 ≤ n→i(m) * 8 + n→i(n) - 2, 0 ≤ i, 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 2 ^ (n→i(m) * 8 + n→i(n) - 1), j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, 8 * (i + 1) < n→i(m) * 8 + n→i(n), n < 8, j < 0, j + 2 ^ (8 * (i + 1) - 1) < 0, m * 8 + n ≤ 9 + 8 * i→n(i) ⊦ m * 8 + n = 0, j + 2 ^ (8 * (i + 1)) = 0, m + 1 = i→n(i + 2), n = 0, m = 0 ∧ n = 1
Proof step 63:
0 ≤ n→i(m) * 8 + n→i(n) - 2, 0 ≤ i, n→i(m) * 8 + n→i(n) - 2 < n→i(m) * 8 + n→i(n) - 1, j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, 8 * (i + 1) < n→i(m) * 8 + n→i(n), n < 8, j < 0, j + 2 ^ (8 * (i + 1) - 1) < 0, m * 8 + n ≤ 9 + 8 * i→n(i) ⊦ m * 8 + n = 0, j + 2 ^ (8 * (i + 1)) = 0, m + 1 = i→n(i + 2), n = 0, m = 0 ∧ n = 1

Rule argument

seq: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0) subst: [j0, j] → [n→i(m) * 8 + n→i(n) - 1, n→i(m) * 8 + n→i(n) - 2] rotate: F spec: int-pot inst: name: ls-pos-2pot

Additional information

Used terms: n→i(m) * 8 + n→i(n) - 1, n→i(m) * 8 + n→i(n) - 2