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Proof step 11 from proof sum-in-not-ls (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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