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Proof step 13 from proof mult-ass (previous step)

0 < j1, 0 < j0, 0 < j ⊦ j = 0, j0 = 0, rational(i * i0, j * j0) * rational(i1, j1) = rational(i, j) * rational(i0, j0) * rational(i1, j1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ j1 ≠ 0 ∧ j2 ≠ 0 → rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)
Proof step 15:
j0 ≠ 0 ∧ j1 ≠ 0, 0 < j1, 0 < j0, 0 < j ⊦ j = 0, j0 = 0, rational(i * i0, j * j0) * rational(i1, j1) = rational(i, j) * rational(i0 * i1, j0 * j1)

Rule argument

name: mult-def-03 rotate: F subst: [j2, i2, j1, i1] → [j1, i1, j0, i0]

Additional information

Used terms: j1, i1, j0, i0