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Proof step 1 from proof ls-def (conclusion)

⊦ 0 < j ∧ 0 < j0 → (rational(i, j) < rational(i0, j0) ↔ i * j0 < i0 * j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 < j, 0 < j0 ⊦ (rational(i, j) - rational(i0, j0)).num < 0 ↔ ¬ i0 * j ≤ i * j0

Rule argument

Additional information

Used simplifier rules: Ls-def: ⊦ ri < rj ↔ (ri - rj).num < 0;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ ¬ i < j ↔ j ≤ i;