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Proof step 27 from proof max-sort-sublist (previous step)

max(x1) < a, ∀ x0. x1 + x0 = [] ∨ max(x1 + x0) = max(x1) ∨ max(x1 + x0) = max(x0) ⊦ max(x1 + x0) = a, x1 + x0 = [], max(x1 + x0) = max(x0), x1 = [], max(x1 + x0) < a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
max(x1) < a, a < max(x1 + x0), max(x1) < max(x1 + x0), ∀ x0. x1 + x0 = [] ∨ max(x1 + x0) = max(x1) ∨ max(x1 + x0) = max(x0) ⊦ max(x1 + x0) = a, x1 + x0 = [], max(x1 + x0) = max(x0), x1 = []

Rule argument

Additional information

Used simplifier rules: transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem%sls: ⊦ a ≠ b → (¬ a < b ↔ b < a); from specification oelem