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Proof step 1 from proof div-nearer-zero (conclusion)

j ≠ 0 ⊦ abs(i / j * j) ≤ abs(i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
abs(i) < abs(i) / abs(j) * abs(j) ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: abs: j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j);%lels-01: ⊦ ¬ i ≤ j ↔ j < 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%abs-eqall: ⊦ abs(i * j) = abs(i) * abs(j); from specification int-mult