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Proof step 2 from proof nextl-lemma-butlast-nonempty (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ n. ∃ lf. lf(0) = a ' ∧ (∀ m. m < n → lf(m + 1) = nextl(m, lf(m).last) ∧ lf(m) ≠ []), ∀ n, a. nextl(n, a) ≠ [] ⊦ ∃ lf. lf(0) = a ' ∧ (∀ n. lf(n + 1) = nextl(n, lf(n).last) ∧ lf(n) ≠ [])

Proof step 2 from proof nextl-lemma-butlast-nonempty (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information