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Proof step 1 from proof elim-list-c (conclusion)

x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ x = x.first + x.rest, x = []

Rule argument

Additional information

Used simplifier rules: sel-1: ⊦ (a + x).first = a;%sel-2: ⊦ (a + x).rest = x;