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Proof step 9 from proof sum-in-not-ls (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; 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%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs