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Proof step 1 from proof modeq-pos-02 (conclusion)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 2:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)
Proof step 3:
j0 = i1 * j + j1 ∧ 0 ≤ j1 ∧ j1 < j, 0 ≤ i0 * j + j0, 0 < j, 0 ≤ j0 ⊦ (i0 * j + j0) % j = j1

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] → [j0, j, i, j1] flags: rewrite, current

Additional information

Used terms: j0, j, i, j1