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Proof step 11 from proof modmod-add (previous step)

j0 + i0 = i2 * j + j1, 0 ≤ i1 * j + i0 + j0, 0 ≤ i0 + j0, 0 ≤ j1, j1 < j, 0 ≤ j0 + i0, 0 ≤ i0, 0 ≤ j0, j0 < j, 0 ≤ i1, 0 < j ⊦ j1 = (i0 + j0) % j

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)
Proof step 13:
i0 + j0 = i3 * j + j2 ∧ 0 ≤ j2 ∧ j2 < j, j0 + i0 = i2 * j + j1, 0 ≤ i1 * j + i0 + j0, 0 ≤ i0 + j0, 0 ≤ j1, j1 < j, 0 ≤ j0 + i0, 0 ≤ i0, 0 ≤ j0, j0 < j, 0 ≤ i1, 0 < j ⊦ j1 = j2

Rule argument

spec: int-div inst: name: div-elim-pos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [i0 + j0, j, i2, j2] flags: rewrite, current

Additional information

Used terms: i0 + j0, j, i2, j2