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Proof step 5 from proof modmod-pos (previous step)

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

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 = i1 * j0 + j2 ∧ 0 ≤ j2 ∧ j2 < j0 ∧ 0 ≤ i1, j1 < j, 0 < j, 0 < j0, 0 ≤ j1, 0 ≤ i0 ⊦ (i0 * j + j1) % (j * j0) = j1 + j2 * 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] → [i0, j0, i, j2] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i0, j0, i, j2