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Proof step 5 from proof ls-01 (previous step)

0 < i / j0, 0 ≤ i1, j1 < j0, 0 ≤ j1, i1 < i / j0, i0 ≤ j0, i ≤ i1 * i0 + j1, j1 < i0, 0 < i0, 0 < j0, 0 ≤ i ⊦ i0 = 0, j0 = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-elim-pos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [i, j0, i2, j] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i, j0, i2, j