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Proof step 8 from proof factor-rat-02 (previous step)

0 < j, i1 < 0 ⊦ i1 = 0, rational(~(i1 * i), ~(i1 * j)) = rational(i, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ~ i * j = ~(i * j)
Proof step 10:
0 < j, i1 < 0 ⊦ i1 = 0, rational(~ i1 * i, ~(i1 * j)) = rational(i, j)

Rule argument

seq: ⊦ ~ i * j = ~(i * j) subst: [j, i] → [i, i1] rotate: T spec: int-mult inst: name: minus-left

Additional information

Used terms: i, i1