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Proof step 16 from proof max-ordered (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
max((a ' + x2) + x0) = max(a ' + x2), ordered≤(x0), x1 ⊑ x0, ∀ x0, x1. max(x2 + x0) = max(x2) ∧ ordered≤(x0) ∧ x1 ⊑ x0 → max(x2 + x1) = max(x2) ∨ x2 = [] ⊦ x2 + x1 = [], max(x2 + x1) = max(a ' + x2), max(x2 + x1) < a

Proof step 16 from proof max-ordered (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information