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Proof step 9 from proof factor-rat-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: factor-rat-02 rotate: F subst: [j, i, i1] → [~ j, ~ i, ~ i1]

Additional information

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