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Proof step 5 from proof div-add1-posneg-neg (previous step)

i % j = 0, abs(j0) < j, (i + i1 * j + j0) + 1 < j, 0 ≤ i, (i1 * j + j0) + 1 < j, 0 < j, j0 ≤ 0, j0 < j, i1 ≤ 0, i1 < j, i1 * j + j0 < 0, i1 * j + j0 < j, i + i1 * j + j0 < 0, i + i1 * j + j0 < j ⊦ (i + i1 * j + j0) / j = i / j + i1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-elim-pospos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0) subst: [i, j, i0, j0] → [i, j, i0, j1] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i, j, i0, j1