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Proof step 17 from proof add-def-02 (previous step)

i3 * j1 = 0, gcd(i1, j1) = 1, 0 < i3, 1 < i, 0 < i, 0 < j1, ∀ 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) ⊦ i = 0, rational(i0, i3) + rational(i1, j1) = rational(i * (j1 * i0 + i1 * i3), 0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0 subst: [j, i] → [j1, i3] rotate: F spec: int-mult inst: name: zero-eq

Additional information

Used simplifier rules: ⊦ i * 0 = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ gcd(i, 0) = abs(i); Used terms: j1, i3