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Proof step 10 from proof add-def-02 (previous step)

gcd(i1, j1) = 1, 0 < j1, 0 < i, 1 < i, 0 < i3, ∀ j2, j1, i4, i3. i→n(i3) + i→n(i4) < i→n(i1) + i→n(i * i0) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) + rational(i4, j2) = rational(i3 * j2 + j1 * i4, j1 * j2) ⊦ rational(i0, i3) + rational(i1, j1) = rational(i * (j1 * i0 + i1 * i3), j1 * i * i3)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i * j = j * i
Proof step 12:
gcd(i1, j1) = 1, 0 < j1, 0 < i, 1 < i, 0 < i3, ∀ j2, j1, i4, i3. i→n(i3) + i→n(i4) < i→n(i1) + i→n(i * i0) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) + rational(i4, j2) = rational(i3 * j2 + j1 * i4, j1 * j2) ⊦ rational(i0, i3) + rational(i1, j1) = rational(i * (j1 * i0 + i1 * i3), (i * i3) * j1)

Rule argument

seq: ⊦ i * j = j * i subst: [j, i] → [i * i3, j1] rotate: F spec: int-mult inst: name: commutativity

Additional information

Used terms: i * i3, j1