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Proof step 3 from proof ole-rec (previous step)

⊦ x.tail = [], ordered≤(x) ↔ ¬ x.tail.head < x.head ∧ ordered≤(x.tail), x = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
x = a + y ⊦ ordered≤(x) ↔ ¬ y.head < a ∧ ordered≤(y), x = [], y = []

Rule argument

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

Additional information

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