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Proof step 9 from proof ordered-max (previous step)

max(x0) = x0.last, x0.last < a, ordered≤(x0) ⊦ a = x0.last, x0 = [], x0.head < a

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
max(x0) = x0.last, x0 = a0 + y, x0.last < a, ordered≤(x0) ⊦ a = x0.last, x0 = [], a0 < a

Rule argument

spec: list-data name: elim-list-c seq: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y subst: [x, a, y] → [x0, a0, y]

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: x0, a0, y