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Proof step 20 from proof min-rec (previous step)

min(i ' + ints) ≤ i, min(ints) ≤ i, min(ints) ∈ ints → min(i ' + ints) ≤ min(ints), ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0, ∀ 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 21:
min(i ' + ints) ≤ i, min(ints) ≤ i, min(i ' + ints) < min(ints), min(i ' + ints) < i, ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0, ∀ i. i ∈ ints → min(ints) ≤ i ⊦ ints = [], min(i ' + ints) = min(ints)

Rule argument

Additional information

Used simplifier rules: min-in: ⊦ min(ints) ∈ ints ↔ ints ≠ [];%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs