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Proof step 9 from proof mod2-add-neg (previous step)

0 ≤ i + i0 * 2, i < 0, i < i0 * 2, 0 ≤ i0, 0 < i0 ⊦ i % 2 + (i + i0 * 2) % 2 = 0, i = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j)
Proof step 11:
i = i1 * 2 + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 2 ∧ 0 < 2, 0 ≤ i + i0 * 2, i < 0, i < i0 * 2, 0 ≤ i0, 0 < i0 ⊦ j0 + (i + i0 * 2) % 2 = 0, i = 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, 2, i1, j] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: i, 2, i1, j