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Proof step 13 from proof div-eq-zero-01 (previous step)

i / j = 0, i < j, i < 0 ⊦ 0 = j, 0 < abs(j) + i, 0 < j ∧ i < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
i / j = 0, j < 0, i < j, i < 0 ⊦ 0 < i - j

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ i < j → ¬ j < i; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + ~ j = i - j; (s)% ⊦ i < 0 → abs(i) = ~ i; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)