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Proof step 3 from proof mult-def-03 (previous step)

¬(0 < j1 ∧ 0 < j2) ⊦ j1 ≠ 0 ∧ j2 ≠ 0 → rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2), j2 = 0, j1 = 0, ¬ j1 < 0 ∧ ¬ j2 < 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;