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Proof step 10 from proof mult-ass (previous step)

0 < j, 0 < j0, 0 < j1 ⊦ (rational(i, j) * rational(i0, 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 11:
⊦ j1 ≠ 0 ∧ j2 ≠ 0 → rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)
Proof step 12:
j ≠ 0 ∧ j0 ≠ 0, 0 < j, 0 < j0, 0 < j1 ⊦ rational(i * i0, j * j0) * rational(i1, j1) = rational(i, j) * rational(i0, j0) * rational(i1, j1)

Rule argument

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

Additional information

Used terms: j0, i0, j, i