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Proof step 3 from proof mult-def-02 (previous step)

0 < j1, 0 < j2, ∀ j2, j1, i, i0. i→n(i0) + i→n(i) < i→n(i1) + i→n(i2) → 0 < j1 ∧ 0 < j2 → rational(i0, j1) * rational(i, j2) = rational(i0 * i, j1 * j2) ⊦ rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
gcd(i1, j1) = 1, gcd(i2, j2) = 1, 0 < j1, 0 < j2 ⊦ rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)
Proof step 5:
¬(gcd(i1, j1) = 1 ∧ gcd(i2, j2) = 1 ∧ 0 < j1 ∧ 0 < j2), 0 < j1, 0 < j2, ∀ j2, j1, i, i0. i→n(i0) + i→n(i) < i→n(i1) + i→n(i2) → 0 < j1 ∧ 0 < j2 → rational(i0, j1) * rational(i, j2) = rational(i0 * i, j1 * j2) ⊦ rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)

Rule argument

name: mult-def-01 rotate: F subst: [j2, i2, j1, i1] → [j2, i2, j1, i1]

Additional information

Used simplifier rules: ⊦ i * j = j * i; Used terms: j2, i2, j1, i1