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Proof step 2 from proof div-eq (previous step)

j | i ⊦ i / j = i0 ↔ i = i0 * j, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
j | i ⊦ i % j = 0, j = 0

Rule argument

Additional information

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