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Proof step 1 from proof div-mult-le-01 (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 < j, 0 ≤ i, i ≤ j * i / j, 0 ≤ i / j ⊦ i % j = 0

Rule argument

Additional information

Used simplifier rules: divmult: j ≠ 0 ⊦ i % j = 0 → i / j * j = i;%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%ler: ⊦ i ≤ i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult