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Proof step 4 from proof mult-def-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ j < 0 → rational(i, j) = rational(~ i, abs(j))
Proof step 6:
¬ j1 < 0 ⊦ rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2), j2 = 0, j1 = 0, ¬ j1 < 0 ∧ ¬ j2 < 0
Proof step 17:
j1 < 0 ⊦ rational(~ i1, abs(j1)) * rational(i2, j2) = rational(i1 * i2, j1 * j2), j2 = 0, j1 = 0, ¬ j1 < 0 ∧ ¬ j2 < 0

Rule argument

name: denom-neg rotate: F subst: [j, i] → [j1, i1]

Additional information

Used terms: j1, i1