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Proof step 11 from proof div-ls-zero (previous step)

0 - j0 < j, 0 < j, i0 < j, j0 < j, i0 * j + j0 < 0, j0 < 0, i0 ≤ 0, j0 ≤ 0 ⊦ i0 < 0 ↔ ¬ 0 < j * (i0 + 1) + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
i0 * j + j0 < 0, j0 < j, i0 < j, 0 < j, j0 < 0, 0 < j + j0, i0 ≤ 0 ⊦ i0 < 0 ↔ ¬ 0 < j * (i0 + 1) + j0

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ 0 - i = ~ i; (s)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)