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Proof step 7 from proof transitivity (previous step)

∃ i, j. rj = rational(i, j) ∧ 0 < j, rj < rj0, rational(i, j) < rj, 0 < j ⊦ rational(i, j) < rj0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 < j, rational(i0, j0) < rj0, i * j0 < i0 * j, 0 < j0 ⊦ rational(i, j) < rj0

Rule argument

Additional information

Used simplifier rules: ls-def: ⊦ 0 < j ∧ 0 < j0 → (rational(i, j) < rational(i0, j0) ↔ i * j0 < i0 * j);% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)