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Proof step 21 from proof sort-max-last (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: ordered-max seq: ⊦ x ≠ [] ∧ ordered≤(x) → max(x) = x.last subst: [x] → [sort(x1 + x0) + a '] flags: rewrite, current

Additional information

Used simplifier rules: e-02: ⊦ x + a ' ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%last-def: ⊦ (x + a ').last = a; from specification list-last%irreflexivity: ⊦ ¬ a < a; from specification oelem Used terms: sort(x1 + x0) + a '