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Proof step 7 from proof sort-max-max-list (previous step)

ordered≤(sort(x0)) ∧ ¬ a < max(sort(x0)), max(x0) < a, max(sort(x0)) = max(x0) ⊦ max(sort(x0) + a ') = a, x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
max(sort(x0)) = max(x0), max(x0) < a ⊦ x0 = [], max(sort(x0) + a ') = a

Rule argument

Additional information

Used simplifier rules: ls-le: ⊦ a < b → (¬ b < a ↔ true); from specification oelem%nen: ⊦ ¬ b < a ∧ a = c → ¬ b < c; (forward) from specification oelem%lel: ⊦ a < b ∧ a = c → c < b; (forward) from specification oelem%Ordered: ⊦ ordered≤(sort(x)); from specification olist-sort