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Proof step 30 from proof div-eq-zero-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
i / j = 0, j < 0, 0 ≤ i + j, 0 ≤ i ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i < j → ¬ j < i; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < ~ j ↔ i + j < 0; (s)% ⊦ i < 0 → abs(i) = ~ i; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)