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Proof step 4 from proof mult-ls (previous step)

i / j < j, i / j < ~1, i0 < 0, i0 < j, i0 + 1 < j, i < j, i < 0, 0 < j, i0 * j ≤ i, i / j < i0, i + 1 < j, i / j < 0 ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j)
Proof step 6:
i = i1 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j, i1 < j, i1 < ~1, i0 < 0, i0 < j, i0 + 1 < j, i < j, i < 0, 0 < j, i0 * j ≤ i, i1 < i0, i + 1 < j, i1 < 0 ⊦

Rule argument

spec: int-div inst: name: div-elim2 seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j) subst: [i, j, i0, j0] → [i, j, i1, j0] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: i, j, i1, j0