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Proof step 48 from proof int2bytes-len-neg (previous step)

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

Proof step 49:
j ≤ i, 0 ≤ j ⊦ i→n(i - j) = i→n(i) - i→n(j)
Proof step 50:
1 ≤ 8 * (i + 1) ∧ 0 ≤ 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, i→n(i) * 8 < i→n(8 * (i + 1)) - i→n(1), j < ~1, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, m * 8 + n ≤ (i→n(8 * (i + 1)) - i→n(1)) + 1, 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 ^ (8 * i) = 0, m = i→n(i), n = 0, 8 * (i + 1) = 1, m = 0 ∧ n = 1

Rule argument

seq: j ≤ i, 0 ≤ j ⊦ i→n(i - j) = i→n(i) - i→n(j) subst: [j, i] → [1, 8 * (i + 1)] rotate: F spec: intnat inst: name: sub

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j * j0 = (i * j) * j0; Used terms: 1, 8 * (i + 1)