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Proof step 14 from proof div-nearer-zero (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
i / abs(j) * abs(j) < i, i < 0 ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ ~ j < ~ i ↔ i < j; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ ~ i * j = ~(i * j); (s)% ⊦ abs(i) = 0 ↔ i = 0; (s)% ⊦ 0 - i = ~ i; (s)