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Proof step 3 from proof max-append (previous step)

⊦ x + x0 = [], max(x + x0) = max(x0), max(x + x0) = max(x)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ x0. x1 + x0 = [] ∨ max(x1 + x0) = max(x0) ∨ max(x1 + x0) = max(x1) ⊦ (a + x1) + x0 = [], max((a + x1) + x0) = max(a + x1), max((a + x1) + x0) = max(x0)

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;% ⊦ [] + x = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list