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Proof step 41 from proof int2bytes-len-neg-01 (previous step)

n0 < 2 + i→n(i), 0 ≤ i, 0 < j + 2 ^ (8 * (i + 1)), j + 2 ^ (8 * (i + 1) - 1) < 0, j + 2 ^ (n→i(n0) * 8 - 2) < 0, 0 ≤ 2 ^ (n→i(n0) * 8 - 1) + j, j < 0, i + 1 < n→i(n0) ⊦ n0 = 0, n0 * 8 = 1, n0 = 2 + i→n(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n subst: [n, i] → [n0, i + 1] rotate: F spec: intnat inst: name: num-n2i-ls-02

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1;% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m +1 = m + 1;% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 ≤ i → abs(i) = i;% ⊦ ¬ i < i;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: n0, i + 1