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Proof step 42 from proof nextnli-lemma (previous step)

m ≠ n0, m ≤ n0, ∀ m. m < n0 → lf(m + 1) = nextnli(lf(m), m) ⊦ lf(m + 1) = nextnli((m = n0 + 1 ⊃ nextnli(lf(n0), n0);lf(m)), m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
m < n0, ∀ m. m < n0 → lf(m + 1) = nextnli(lf(m), m) ⊦ lf(m + 1) = nextnli((m = n0 + 1 ⊃ nextnli(lf(n0), n0);lf(m)), m), m = n0, n0 = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat