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Proof step 19 from proof min-del-nlz-01 (previous step)

¬ i < min(ints0 -l i0), 0 < min(i, min(ints0)), 0 < min(ints0), min(ints0 -l i0) < 0, min(ints0 -l i0) < min(i, min(ints0)), min(ints0 -l i0) < min(ints0), ∀ i0. ¬ min(ints0 -l i0) < 0 ⊦ ints0 = [], i0 = i, ints0 -l i0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
0 < min(i, min(ints0)), 0 < min(ints0), min(ints0 -l i0) ≤ i, min(ints0 -l i0) < 0, min(ints0 -l i0) < min(i, min(ints0)), min(ints0 -l i0) < min(ints0), ∀ i0. ¬ min(ints0 -l i0) < 0 ⊦ ints0 = [], i0 = i, ints0 -l i0 = []

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs