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Proof step 25 from proof int2bytes-rec-neg-04 (previous step)

i→n(i * 8) % 8 = 0, 0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ j0 = 0, i = 0, mklist(i2b(0), i→n(i * 8) / 8) = fix(i→n(i) + 1, i2b(0) ').rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
0 ≤ i, 0 ≤ j ⊦ i→n(i) * i→n(j) = i→n(i * j)
Proof step 27:
0 ≤ i ∧ 0 ≤ 8, (i→n(i) * i→n(8)) % 8 = 0, 0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ j0 = 0, i = 0, mklist(i2b(0), (i→n(i) * i→n(8)) / 8) = fix(i→n(i) + 1, i2b(0) ').rest

Rule argument

seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i) * i→n(j) = i→n(i * j) subst: [j, i] → [8, i] rotate: T spec: intnat inst: name: i2np

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: 8, i