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Proof step 5 from proof sum-in-not-ls (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
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 ≠ i ∧ ¬ j ∈ ints0

Proof step 5 from proof sum-in-not-ls (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information