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Proof step 3 from proof nummult-le-03 (previous step)

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

Heuristic var elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j)
Proof step 5:
j = i1 * i + j0 ∧ j0 ≤ 0 ∧ abs(j0) < i, j < i, j < 0, 0 < i, j + 1 < i ⊦ j ≤ i * i0 ↔ i1 ≤ i0

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] → [j, i, 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: j, i, i1, j0