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Proof step 22 from proof min-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
min(i ' + ints) ≤ i, min(ints) ≤ i, min(i ' + ints) < min(ints), min(i ' + ints) < i, ∀ i. i ∈ ints → min(ints) ≤ i, ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0 ⊦ ints = [], min(i ' + ints) = min(ints), min(i ' + ints) ∈ ints

Rule argument

Additional information

Used simplifier rules: ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs