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Proof step 8 from proof product-negative (previous step)

0 < i, Π ints0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0 ⊦ Π ints0 < 0 ∧ (i0 ∈ ints0 → 0 ≤ i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i0 ∈ ints0, 0 < i, Π ints0 < 0, Π ints0 < i, i0 < 0, i0 < i, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs