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Proof step 4 from proof min-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ i0. i0 = i ∨ i0 ∈ ints → min(i ' + ints) ≤ i0 ⊦ ints = [], min(i ' + ints) = min(i, min(ints))

Rule argument

Additional information

Used simplifier rules: min-in: ⊦ min(ints) ∈ ints ↔ ints ≠ [];%in-17: ⊦ i ∈ i0 ' ↔ i = i0; from specification list[intlista]%in-append: ⊦ i ∈ ints + ints0 ↔ ¬ ¬(i ∈ ints ∨ i ∈ ints0); from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%e-01: ⊦ i ' + ints ≠ []; from specification list[intlista]%c: ⊦ i + ints = i ' + ints; from specification list[intlista]