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Proof step 7 from proof totality (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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 * j0 = (i * j) * j0;% ⊦ i ≤ i;% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0);% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;