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Proof step 7 from proof ls-def (previous step)

j ≠ 0 ∧ j0 ≠ 0, 0 < j0, 0 < j ⊦ rational(i * j0 + j * ~ i0, j * j0).num < 0 ↔ ¬ i0 * j ≤ i * j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 < j0, 0 < j ⊦ j0 = 0, j = 0, rational(i * j0 - i0 * j, j * j0).num < 0 ↔ ¬ i0 * j ≤ i * j0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + ~ j = i - j;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ ~ i * j = ~(i * j);