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Proof step 2 from proof div-mult-le-01 (previous step)

0 < j, 0 ≤ i ⊦ i ≤ j * i / j ↔ i % j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: divmult: j ≠ 0 ⊦ i % j = 0 → i / j * j = i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)%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% ⊦ i ≤ i; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult