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Proof step 8 from proof min-del-nlz-01 (previous step)

ints0 ≠ [], min((i ' + ints0) -l i0) < 0, min((i ' + ints0) -l i0) < min(i, min(ints0)), 0 < min(i, min(ints0)), 0 < min(ints0) → (∀ i0. ¬ min(ints0 -l i0) < 0) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
min((i ' + ints0) -l i0) < 0, min((i ' + ints0) -l i0) < min(i, min(ints0)), min((i ' + ints0) -l i0) < min(ints0), 0 < min(i, min(ints0)), 0 < min(ints0), ∀ i0. ¬ min(ints0 -l i0) < 0 ⊦ ints0 = []

Rule argument

Additional information

Used simplifier rules: min-c: ⊦ min(i, j) = min(j, i); from specification int-min%min-a: ⊦ min(i, min(j, j0)) = min(min(i, j), j0); from specification int-min%min-03: ⊦ ¬ i < min(i, j); from specification int-min%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs