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Proof step 6 from proof sort-max-max-list (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ordered≤(x0) ∧ ¬ a < max(x0) → ins≤(a, x0) = x0 + a '
Proof step 8:
max(sort(x0)) = max(x0), max(x0) < a, ordered≤(sort(x0)) ⊦ max(sort(x0) + a ') = a, x0 = [], a < max(sort(x0))

Rule argument

spec: <toplevel> name: ins-max seq: ⊦ ordered≤(x0) ∧ ¬ a < max(x0) → ins≤(a, x0) = x0 + a ' subst: [x0, a] → [sort(x0), a] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ordered≤(sort(x)); (s)%transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem%lel: ⊦ a < b ∧ a = c → c < b; (forward) from specification oelem% ⊦ ¬ a < a; (s) Used terms: sort(x0), a