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Proof step 8 from proof div-nearer-zero (previous step)

0 < i / abs(j) * abs(j), i < i / abs(j) * abs(j), 0 ≤ i ⊦ j = 0, j < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i < i / j * j, 0 < i / j, 0 < j, 0 ≤ i ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ 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 < i → (0 < i * j ↔ 0 < j); (s)% ⊦ ¬ j < 0 → abs(j) = j; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)