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Proof step 7 from proof sum-not-ls-zero (previous step)

i + Σ ints0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0 ⊦ i0 ∈ ints0 → 0 ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i0 ∈ ints0, i + Σ ints0 < 0, i0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0 ⊦

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