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Proof step 3 from proof fr-04 (previous step)

x.head = y.head, x.tail = y.tail ⊦ x = [], x = y, y = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y

Rule argument

spec: <toplevel> name: elim-list-c seq: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y subst: [x, a, y] → [x, a, y0] flags: <rotated> <all paths>

Additional information

Used simplifier rules: fr-02: ⊦ x ≠ [] → x.head + x.tail = x; Used terms: x, a, y0