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Proof step 18 from proof sort-max-max-list (previous step)

max(sort(x0)) = max(x0) ⊦ max(ins≤(a, sort(x0))) = max(x0), x0 = [], max(x0) < a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ ¬ max(x) < a ∧ x ≠ [] → max(ins≤(a, x)) = max(x)

Rule argument

spec: inst: name: max-ins seq: ⊦ ¬ max(x) < a ∧ x ≠ [] → max(ins≤(a, x)) = max(x) subst: [x, a] → [sort(x0), a] flags: rewrite, current

Additional information

Used simplifier rules: emptyp: ⊦ sort(x) = [] ↔ x = []; from specification olist-sort%lel: ⊦ a < b ∧ a = c → c < b; (forward) from specification oelem%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem Used terms: sort(x0), a