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Proof step 34 from proof nextl-lemma-butlast-nonempty (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 35:
∀ n, a. nextl(n, a) ≠ [] ⊦ ∃ lf. lf(0) = a ' ∧ (∀ m. m < 0 → lf(m + 1) = nextl(m, lf(m).last) ∧ lf(m) ≠ [])
Proof step 37:
∀ 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. m < n0 +1 → lf(m + 1) = nextl(m, lf(m).last) ∧ lf(m) ≠ [])

Rule argument

indvar: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;