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Proof step 6 from proof max-ins-max-last-sort (previous step)

a < max(sort(x0)), max(x0) < max(sort(x0)) ⊦ ins≤(a, sort(x0)) = sort(x0) + a ', a < max(x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ x ≠ [] → max(sort(x)) = max(x)

Rule argument

spec: <toplevel> name: sort-max-max-list seq: ⊦ x ≠ [] → max(sort(x)) = max(x) subst: [x] → [x0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ sort([]) = []; (s)% ⊦ ins≤(a, []) = a '; (s)% ⊦ [] + x = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' = b ' ↔ a = b; (s) Used terms: x0