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Proof step 7 from proof max-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ i. i ∈ ints → i ≤ max(ints), ∀ i0. i0 = i ∨ i0 ∈ ints → i0 ≤ max(i ' + ints) ⊦ ints = [], max(i ' + ints) = max(i, max(ints))

Rule argument

Additional information

Used simplifier rules: max-in-01: ⊦ max(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]