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Proof step 9 from proof nextl-lemma (previous step)

∀ m, n1, n2. m ≤ n1 ∧ n1 ≤ n2 → lfgen(n1)(m) = lfgen(n2)(m), lfgen(0)(0) = nextl(0, a), ∀ n. lfgen(n)(0) = nextl(0, a) ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m + 1, lfgen(n)(m).last)) ⊦ lfgen(n + 1)(n + 1) = nextl(n + 1, lfgen(n)(n).last)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
lfgen(0)(0) = nextl(0, a), ∀ m, n1, n2. m ≤ n1 ∧ n1 ≤ n2 → lfgen(n1)(m) = lfgen(n2)(m), ∀ n. lfgen(n)(0) = nextl(0, a) ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m + 1, lfgen(n)(m).last)) ⊦ lfgen(n + 1)(n + 1) = nextl(n + 1, lfgen(n)(n).last)

Proof step 9 from proof nextl-lemma (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information