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Proof step 6 from proof nextli-lemma (previous step)

lfgen(0)(0) = [], ∀ n. lfgen(n)(0) = [] ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextli(lfgen(n)(m))) ⊦ lfgen(n + 1)(n + 1) = nextli(lfgen(n)(n))

User applied rule cut formula

And obtained the following new goals

Proof step 7:
∀ m, n1, n2. m ≤ n1 ∧ n1 ≤ n2 → lfgen(n1)(m) = lfgen(n2)(m), lfgen(0)(0) = [], ∀ n. lfgen(n)(0) = [] ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextli(lfgen(n)(m))) ⊦ lfgen(n + 1)(n + 1) = nextli(lfgen(n)(n))
Proof step 13:
lfgen(0)(0) = [], ∀ n. lfgen(n)(0) = [] ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextli(lfgen(n)(m))) ⊦ ∀ m, n1, n2. m ≤ n1 ∧ n1 ≤ n2 → lfgen(n1)(m) = lfgen(n2)(m), lfgen(n + 1)(n + 1) = nextli(lfgen(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)