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Proof step 11 from proof sort-max-max-list (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
max(sort(x0)) = max(x0), max(x0) < a ⊦ max(sort(x0) + a ') = a, x0 = [], ordered≤(sort(x0) + a ')

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ x + a ' ≠ []; (s)