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Proof step 3 from proof diag-theorem-butlast (previous step)

∀ n, a. nextl(n, a) ≠ [] ⊦ ∃ lf. lf(0) = a ' ∧ (∀ n. lf(n + 1) = nextl(n, lf(n).last) ∧ lf(n) ≠ [])

Lemma nextl-lemma-butlast-nonempty