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Proof step 25 from proof sort-max-last (previous step)

sort(x1 + max(x1 + x0) ' + x0) = sort(x1 + x0) + max(x1 + x0) ', max(x1 + x0) < max(sort(x1 + x0) + max(x1 + x0) '), ordered≤(sort(x1 + x0) + max(x1 + x0) ') ⊦ x1 + x0 = [], ins≤(max(x1 + x0), sort(x1 + x0) + max(x1 + x0) ') = (sort(x1 + x0) + max(x1 + x0) ') + max(x1 + x0) '

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: ordered-max seq: ⊦ x ≠ [] ∧ ordered≤(x) → max(x) = x.last subst: [x] → [sort(x1 + x0) + max(x1 + x0) '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ x + a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ (x + a ').last = a; (s)% ⊦ ¬ a < a; (s) Used terms: sort(x1 + x0) + max(x1 + x0) '