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Proof step 39 from proof nextli-lemma (previous step)

lf(0) = [], ∀ m. m < n0 → lf(m + 1) = nextli(lf(m)) ⊦ (0 = n0 + 1 ⊃ nextli(lf(n0));lf(0)) = [] ∧ (∀ m. ¬ n0 < m → (m + 1 = n0 + 1 ⊃ nextli(lf(n0));lf(m + 1)) = nextli((m = n0 + 1 ⊃ nextli(lf(n0));lf(m))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2