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Proof step 5 from proof mod-add1-negpos-neg (previous step)

i1 * j + i0 < 0, i1 < 0, 0 ≤ i0, 0 < j ⊦ i0 % j = (i1 * j + i0) % j + j, i0 % j = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0)
Proof step 7:
i0 = i2 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i2, i1 * j + i0 < 0, i1 < 0, 0 ≤ i0, 0 < j ⊦ j0 = (i1 * j + i0) % j + j, j0 = 0

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] → [i0, j, i, j0] flags: rewrite, current

Additional information

Used terms: i0, j, i, j0