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

0 ≤ i0, j1 < j * j0, 0 ≤ j1, 0 < j, 0 < j0 ⊦ j1 % j = (i0 * j * j0 + j1) % 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)
Proof step 6:
j1 = i1 * j + j2 ∧ 0 ≤ j2 ∧ j2 < j, 0 ≤ i0, j1 < j * j0, 0 ≤ j1, 0 < j, 0 < j0 ⊦ j2 = (i0 * j * j0 + j1) % j

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] → [j1, j, i, j2] flags: rewrite, current

Additional information

Used terms: j1, j, i, j2