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Proof step 41 from proof nextnli-lemma (previous step)

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

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 42:
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)

Rule argument

pos: right 1

Additional information

Used simplifier rules: eq: ⊦ m = m + n ↔ n = 0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2