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Proof step 34 from proof int2bytes-len-neg (previous step)

j < 0, i→n(8 * i) + 1 < # int2bits(j), 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j ⊦ j + 2 ^ (8 * i) = 0, # int2bits(j) / 8 = i→n(i), # int2bits(j) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ 0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j)
Proof step 36:
0 ≤ 8 ∧ 0 ≤ i, j < 0, i→n(8) * i→n(i) + 1 < # int2bits(j), 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j ⊦ j + 2 ^ (8 * i) = 0, # int2bits(j) / 8 = i→n(i), # int2bits(j) % 8 = 0

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;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: i, 8