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Proof step 31 from proof int2bytes-len-neg (previous step)

0 ≤ i, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1) ⊦ (1 + i→n(8 * i)) / 8 = i→n(i), (1 + i→n(8 * i)) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ 0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j)

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j) subst: [j, i] → [i, 8] rotate: F spec: intnat inst: name: i2n-mult

Additional information

Used simplifier rules: ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;%n ≠ 0 ⊦ (n0 + m * n) / n = n0 / n + m;% ⊦ 0 + m = m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ i→n(i) = i→n(j) ↔ abs(i) = abs(j); Used terms: i, 8