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Proof step 5 from proof factor-rat-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ j < 0 → rational(i, j) = rational(~ i, abs(j))
Proof step 7:
i1 * j < 0, 0 < j, i1 < 0 ⊦ rational(~(i1 * i), abs(i1 * j)) = rational(i, j), i1 = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i1 * j, i1 * i