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Proof step 37 from proof add-def-02 (previous step)

i3 * j2 = 0, 0 < i3, 0 < j2, 1 < i, 0 < i, ∀ 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) ⊦ i = 0, rational(i2, j2) + rational(i0, i3) = rational(i * (i3 * i2 + i0 * j2), 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] → [j2, 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; Used terms: j2, i3