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Proof step 12 from proof sort-max-max-list (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ordered≤(x) ∧ ordered≤(x0) ∧ (x ≠ [] ∧ x0 ≠ [] → ¬ x0.head < x.last) → ordered≤(x + x0)
Proof step 14:
max(sort(x0)) = max(x0), max(x0) < a ⊦ max(sort(x0) + a ') = a, x0 = [], ordered≤(sort(x0) + a '), ordered≤(sort(x0)) ∧ ordered≤(a ') ∧ (sort(x0) ≠ [] ∧ a ' ≠ [] → ¬ a '.head < sort(x0).last)

Rule argument

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

Additional information

Used terms: a ', sort(x0)