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Proof step 14 from proof sum-in-not-ls (previous step)

¬(∀ i. i ∈ ints0 → 0 ≤ i), Σ ints0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0, ∀ j0. ¬ j0 ∈ ints0 ∨ ¬ Σ ints0 < j0 ∨ (∃ i. ¬(i ∈ ints0 → 0 ≤ i)) ⊦ i ∈ ints0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
i0 ∈ ints0, Σ ints0 < 0, i0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0, ∀ j0. ¬ j0 ∈ ints0 ∨ ¬ Σ ints0 < j0 ∨ (∃ i. ¬(i ∈ ints0 → 0 ≤ i)) ⊦ i ∈ ints0

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs