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Proof step 17 from proof i2np (previous step)

i→n(j) * i→n(i1) + i→n(j) = i→n((i1 + 1) * j), 0 ≤ j, 0 ≤ i1, ∀ j0. 0 ≤ j0 → i→n(j0) * i→n(i1) + i→n(j0) = i→n((i1 + 1) * j0) ⊦ i→n(i1) * i→n(j) = i→n(i1 * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 19:
i→n(j) * i→n(i1) + i→n(j) = i→n(i1 * j + 1 * j), 0 ≤ j, 0 ≤ i1, ∀ j0. 0 ≤ j0 → i→n(j0) * i→n(i1) + i→n(j0) = i→n((i1 + 1) * j0) ⊦ i→n(i1) * i→n(j) = i→n(i1 * j)

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j, 1, i1] flags: rewrite

Additional information

Used terms: j, 1, i1