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Proof step 40 from proof nextnli-lemma (previous step)

∀ m. m < n0 → lf(m + 1) = nextnli(lf(m), m) ⊦ (0 = n0 + 1 ⊃ nextnli(lf(n0), n0);lf(0)) = lf(0) ∧ (∀ m. ¬ n0 < m → (m + 1 = n0 + 1 ⊃ nextnli(lf(n0), n0);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 41:
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)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + n = m + n0 ↔ n = n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)