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Proof step 6 from proof i2np (previous step)

0 ≤ j, 0 ≤ i0, ∀ j0. 0 ≤ j0 → i→n(i0) * i→n(j0) = i→n(i0 * j0) ⊦ i→n(j) * i→n(i0) + i→n(j) = i→n((i0 + 1) * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ (i + 1) * j = i * j + j
Proof step 8:
0 ≤ j, 0 ≤ i0, ∀ j0. 0 ≤ j0 → i→n(i0) * i→n(j0) = i→n(i0 * j0) ⊦ i→n(j) * i→n(i0) + i→n(j) = i→n(i0 * j + j)

Rule argument

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

Additional information

Used terms: j, i0