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Proof step 4 from proof sort-max-max-list (previous step)

max(sort(x0)) = max(x0) ∨ x0 = [] ⊦ a + x0 = [], max(sort(a + x0)) = max(a + x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
max(sort(x0)) = max(x0) ⊦ max(ins≤(a, sort(x0))) = (max(x0) < a ⊃ a;max(x0)), x0 = []

Rule argument

Additional information

Used simplifier rules: max-base: ⊦ max(a ') = a;%max-rec: ⊦ x ≠ [] → max(a ' + x) = (max(x) < a ⊃ a;max(x));% ⊦ x + [] = x; (s)% ⊦ ins≤(a, []) = a '; (s)% ⊦ sort([]) = []; (s)% ⊦ a ' + x ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ sort(a ' + x) = ins≤(a, sort(x)); (s)% ⊦ a + x = a ' + x; (s)