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Proof step 4 from proof modmod-add-04 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0)
Proof step 6:
i = i1 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i1, 0 < j, 0 ≤ i, 0 ≤ i0 ⊦ (j0 + i0 % j) % j = (i + i0) % j

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] → [i, j, i1, j0] flags: rewrite, current

Additional information

Used terms: i, j, i1, j0