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Proof step 43 from proof nextnli-lemma (previous step)

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

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 44:
m < n0, ∀ m. m < n0 → lf(m + 1) = nextnli(lf(m), m) ⊦ lf(m + 1) = nextnli(lf(m), m), m = n0, m = n0 + 1

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m = m + n ↔ n = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ m + n < m; (s)