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Proof step 5 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 6:
⊦ x ≠ [] → max(sort(x)) = max(x)

Rule argument

spec: inst: name: sort-max-max-list seq: ⊦ x ≠ [] → max(sort(x)) = max(x) subst: [x] → [x0] flags: rewrite, current

Additional information

Used simplifier rules: empty: ⊦ sort([]) = []; from specification olist-sort%ins-e: ⊦ ins≤(a, []) = a '; from specification olist%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-04: ⊦ a ' = b ' ↔ a = b; from specification list Used terms: x0