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Proof step 8 from proof nextnli-lemma (previous step)

n ≤ n ∧ n ≤ n + 1 → lfgen(n)(n) = lfgen(n + 1)(n), ∀ 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
lfgen(n)(n) = lfgen(n + 1)(n), ∀ 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)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%lep: ⊦ m ≤ m + n; from specification nat%ler: ⊦ m ≤ m; from specification nat