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Proof step 13 from proof mult-def-02 (previous step)

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 * 0) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) * rational(i4, j2) = rational(i3 * i4, j1 * j2) ⊦ rational(i1, j1) * rational(0, i3) = rational(0, j1 * i * i3)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ rational(0, j) = rational(0, 1)
Proof step 15:
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 * 0) → 0 < j1 ∧ 0 < j2 → rational(i3, j1) * rational(i4, j2) = rational(i3 * i4, j1 * j2) ⊦ rational(i1, j1) * rational(0, i3) = rational(0, 1)

Rule argument

name: zero-num rotate: F subst: [j] → [j1 * i * i3]

Additional information

Used terms: j1 * i * i3