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

0 < j, i / j < i0, i < 0, i0 < 0, i0 * j ≤ i ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j)
Proof step 7:
i = i1 * j + j0, i0 < 0, i < 0, i1 < i0, 0 < j, abs(j0) < j, i0 * j ≤ i, j0 ≤ 0 ⊦

Rule argument

spec: <toplevel> 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: <rotated> <all paths>

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s) Used terms: i, j, i1, j0