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Proof step 37 from proof nextl-lemma-butlast-nonempty (previous step)

∀ n, a. nextl(n, a) ≠ [], ∀ nextl, a. (∀ n, a. nextl(n, a) ≠ []) → (∃ lf. lf(0) = a ' ∧ (∀ m. m < n0 → lf(m + 1) = nextl(m, lf(m).last) ∧ lf(m) ≠ [])) ⊦ ∃ lf. lf(0) = a ' ∧ (∀ m. m < n0 +1 → lf(m + 1) = nextl(m, lf(m).last) ∧ lf(m) ≠ [])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
∀ nextl, a. (∀ n, a. nextl(n, a) ≠ []) → (∃ lf. lf(0) = a ' ∧ (∀ m. m < n0 → lf(m + 1) = nextl(m, lf(m).last) ∧ lf(m) ≠ [])), ∀ n, a. nextl(n, a) ≠ [] ⊦ ∃ lf. lf(0) = a ' ∧ (∀ m. ¬ n0 < m → lf(m + 1) = nextl(m, lf(m).last) ∧ lf(m) ≠ [])

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m +1 = m + 1; (s)