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Proof step 54 from proof int2bytes-len-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → (2 ^ i ≤ 2 ^ j ↔ i ≤ j) subst: [j, i] → [8 * (i + 1) - 1, 8 * i] rotate: F spec: int-pot inst: name: two-le

Additional information

Used simplifier rules: ⊦ m * n = n * m;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0; Used terms: 8 * (i + 1) - 1, 8 * i