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Proof step 44 from proof max-ordered (previous step)

max(x2 + x0) = a, max(x2) < max(x2 + x1), a < max(x2 + x1), max(x2) < a, ordered≤(x0), x1 ⊑ x0, ∀ x, x3. max(x2 + x) = max(x2) ∧ ordered≤(x) ∧ x3 ⊑ x → max(x2 + x3) = max(x2) ⊦ x2 + x0 = [], x2 + x1 = [], max(x2 + x1) = a, x2 = [], max(x2 + x0) < a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
max(x2) < max(x2 + x0), max(x2 + x0) < max(x2 + x1), max(x2) < max(x2 + x1), ordered≤(x0), x1 ⊑ x0, ∀ x, x3. max(x2 + x) = max(x2) ∧ ordered≤(x) ∧ x3 ⊑ x → max(x2 + x3) = max(x2) ⊦ x2 + x1 = [], x2 + x0 = [], max(x2 + x1) = max(x2 + x0), x2 = []

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a < a; (s)