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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ordered≤(x) ∧ ordered≤(x0) ∧ (x ≠ [] ∧ x0 ≠ [] → ¬ x0.first < x.last) → ordered≤(x + x0)
Proof step 13:
¬(ordered≤(sort(x0)) ∧ ordered≤(a ') ∧ (sort(x0) ≠ [] ∧ a ' ≠ [] → ¬ a '.first < sort(x0).last)), max(sort(x0)) = max(x0), max(x0) < a ⊦ x0 = [], max(sort(x0) + a ') = a, ordered≤(sort(x0) + a ')

Rule argument

spec: olist inst: name: ordered-append seq: ⊦ ordered≤(x) ∧ ordered≤(x0) ∧ (x ≠ [] ∧ x0 ≠ [] → ¬ x0.first < x.last) → ordered≤(x + x0) subst: [x0, x] → [a ', sort(x0)] flags: rewrite

Additional information

Used terms: a ', sort(x0)