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Proof step 1 from proof modmod-mult-04 (conclusion)

⊦ 0 < j ∧ 0 ≤ i ∧ 0 < j0 → (i % (j * j0)) % j = i % j

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

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, j * j0, i0, j1