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Proof step 27 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) ⊦ gcd(i1, j1) = 1, 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 28:
⊦ gcd(i, j) = 1 ↔ ¬(∃ i1. i1 > 1 ∧ i1 | i ∧ i1 | j)
Proof step 29:
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) ⊦ ∀ i0. ¬(i0 > 1 ∧ i0 | i1 ∧ i0 | j1), rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)

Rule argument

seq: ⊦ gcd(i, j) = 1 ↔ ¬(∃ i1. i1 > 1 ∧ i1 | i ∧ i1 | j) subst: [j, i] → [j1, i1] rotate: F spec: int-gcd inst: name: gcd-one

Additional information

Used terms: j1, i1