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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: ⊦ 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)