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Proof step 32 from proof add-def-02 (previous step)

0 < i, 1 < i, 0 < j2, 0 < i3, ∀ j2, j1, i4, i3. i→n(i3) + i→n(i4) < i→n(i * i0) + i→n(i2) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) + rational(i4, j2) = rational(i3 * j2 + j1 * i4, j1 * j2) ⊦ rational(i2, j2) + rational(i0, i3) = rational(i * (i3 * i2 + i0 * j2), (i * i3) * j2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ i * j * j0 = (i * j) * j0
Proof step 34:
0 < i, 1 < i, 0 < j2, 0 < i3, ∀ j2, j1, i4, i3. i→n(i3) + i→n(i4) < i→n(i * i0) + i→n(i2) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) + rational(i4, j2) = rational(i3 * j2 + j1 * i4, j1 * j2) ⊦ rational(i2, j2) + rational(i0, i3) = rational(i * (i3 * i2 + i0 * j2), i * i3 * j2)

Rule argument

seq: ⊦ i * j * j0 = (i * j) * j0 subst: [j0, j, i] → [j2, i3, i] rotate: T spec: int-mult inst: name: associativity

Additional information

Used terms: j2, i3, i