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Proof step 24 from proof nextl-lemma (previous step)

lfgen(0)(0) = nextl(0, a), m0 < n1, n1 ≤ n0, m0 < n0, lfgen(0)(0) = nextl(0, a) ∧ m0 ≤ n1 ∧ n1 ≤ n0 ∧ m0 ≤ n0 ∧ (∀ n. lfgen(n)(0) = nextl(0, a) ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m + 1, lfgen(n)(m).last))) → lfgen(n1)(m0) = lfgen(n0)(m0), ∀ n. lfgen(n)(0) = nextl(0, a) ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m + 1, lfgen(n)(m).last)) ⊦ lfgen(n1)(m0 + 1) = lfgen(n0)(m0 + 1), n1 = 0, n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
lfgen(0)(0) = nextl(0, a), lfgen(n1)(m0) = lfgen(n0)(m0), m0 < n1, n1 ≤ n0, m0 < n0, ∀ n. lfgen(n)(0) = nextl(0, a) ∧ (∀ m. m < n → lfgen(n)(m + 1) = nextl(m + 1, lfgen(n)(m).last)) ⊦ lfgen(n1)(m0 + 1) = lfgen(n0)(m0 + 1), n1 = 0, n0 = 0

Rule argument

Additional information

Used simplifier rules: lels-03: ⊦ m < n → m ≤ n; from specification nat