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Proof step 5 from proof nextnli-lemma (previous step)

∀ n. lfgen(n)(0) = x ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextnli(lfgen(n)(m), m)) ⊦ lfgen(0)(0) = x ∧ lfgen(n + 1)(n + 1) = nextnli(lfgen(n)(n), n)

User applied rule cut formula

And obtained the following new goals

Proof step 6:
∀ m, n1, n2. m ≤ n1 ∧ n1 ≤ n2 → lfgen(n1)(m) = lfgen(n2)(m), ∀ n. lfgen(n)(0) = x ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextnli(lfgen(n)(m), m)) ⊦ lfgen(0)(0) = x ∧ lfgen(n + 1)(n + 1) = nextnli(lfgen(n)(n), n)
Proof step 14:
∀ n. lfgen(n)(0) = x ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextnli(lfgen(n)(m), m)) ⊦ ∀ m, n1, n2. m ≤ n1 ∧ n1 ≤ n2 → lfgen(n1)(m) = lfgen(n2)(m), lfgen(0)(0) = x ∧ lfgen(n + 1)(n + 1) = nextnli(lfgen(n)(n), n)

Rule argument

fma: ∀ m, n1, n2. m ≤ n1 ∧ n1 ≤ n2 → lfgen(n1)(m) = lfgen(n2)(m)

Additional information

Used formulas: ∀ m, n1, n2. m ≤ n1 ∧ n1 ≤ n2 → lfgen(n1)(m) = lfgen(n2)(m)