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Proof step 2 from proof max-ordered (previous step)

max(x + x0) = max(x), ordered≤(x0), x1 ⊑ x0 ⊦ x = [], max(x + x1) = max(x)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ x0, x1. max(x2 + x0) = max(x2) ∧ ordered≤(x0) ∧ x1 ⊑ x0 → x2 = [] ∨ max(x2 + x1) = max(x2), max((a + x2) + x0) = max(a + x2), ordered≤(x0), x1 ⊑ x0 ⊦ a + x2 = [], max((a + x2) + x1) = max(a + x2)

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;