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Proof step 45 from proof nextli-lemma (previous step)

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

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 46:
lf(0) = [], m < n0, ∀ m. m < n0 → lf(m + 1) = nextli(lf(m)) ⊦ lf(m + 1) = nextli(lf(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)