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Proof step 17 from proof mult-def-03 (previous step)

j1 < 0 ⊦ rational(~ i1, abs(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 18:
0 < j1, 0 < j2 ⊦ rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)
Proof step 19:
¬(0 < abs(j1) ∧ 0 < j2), j1 < 0 ⊦ rational(~ i1, abs(j1)) * rational(i2, j2) = rational(i1 * i2, j1 * j2), j2 = 0, j1 = 0, ¬ j1 < 0 ∧ ¬ j2 < 0
Proof step 23:
0 < abs(j1) ∧ 0 < j2, j1 < 0 ⊦ rational(~ i1 * i2, abs(j1) * j2) = rational(i1 * i2, j1 * j2), j2 = 0, j1 = 0, ¬ j1 < 0 ∧ ¬ j2 < 0

Rule argument

name: mult-def-02 rotate: F subst: [j2, i2, j1, i1] → [j2, i2, abs(j1), ~ i1]

Additional information

Used terms: j2, i2, abs(j1), ~ i1