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Proof step 8 from proof ls-def (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
i * j0 = i1 + i0 * j, 0 < j0, 0 < j ⊦ j0 = 0, j = 0, rational(i1, j * j0).num < 0 ↔ ¬ i0 * j ≤ i * j0

Rule argument

seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i * j0, i0 * j, i1] rotate: T spec: int-abs inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i * j0, i0 * j, i1