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Proof step 16 from proof int2bytes-len-neg-01 (previous step)

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 = i→n(i + 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j)
Proof step 18:
0 ≤ i ∧ 0 ≤ 2, 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 = i→n(i) + i→n(2)

Rule argument

seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j) subst: [j, i] → [2, i] rotate: F spec: intnat inst: name: add-01

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 2, i