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Proof step 12 from proof min-rec (previous step)

¬ ¬ i < min(ints), min(i ' + ints) ≤ i, ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0, ∀ i. i ∈ ints → min(ints) ≤ i ⊦ ints = [], min(i ' + ints) = min(i, min(ints))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
i < min(ints), min(i ' + ints) < i, min(i ' + ints) < min(ints), ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0, ∀ i. i ∈ ints → min(ints) ≤ i ⊦ ints = [], min(i ' + ints) = i

Rule argument

Additional information

Used simplifier rules: transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%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-left: ⊦ j < i → min(j, i) = j; from specification int-min