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Proof step 1 from proof nextnli-lemma (conclusion)

⊦ ∃ lf. lf(0) = x ∧ (∀ n. lf(n + 1) = nextnli(lf(n), n))

User applied rule cut formula

And obtained the following new goals

Proof step 2:
∀ n. ∃ lf. lf(0) = x ∧ (∀ m. m < n → lf(m + 1) = nextnli(lf(m), m)) ⊦ ∃ lf. lf(0) = x ∧ (∀ n. lf(n + 1) = nextnli(lf(n), n))
Proof step 31:
⊦ ∀ n. ∃ lf. lf(0) = x ∧ (∀ m. m < n → lf(m + 1) = nextnli(lf(m), m)), ∃ lf. lf(0) = x ∧ (∀ n. lf(n + 1) = nextnli(lf(n), n))

Rule argument

fma: ∀ n. ∃ lf. lf(0) = x ∧ (∀ m. m < n → lf(m + 1) = nextnli(lf(m), m))

Additional information

Used formulas: ∀ n. ∃ lf. lf(0) = x ∧ (∀ m. m < n → lf(m + 1) = nextnli(lf(m), m))