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Proof step 53 from proof nextl-lemma-butlast-nonempty (previous step)

lf(m) = [], lf(0) = a ', m = m0 + 1, m ≤ n0, m0 < n0 → lf(m0 + 1) = nextl(m0, lf(m0).last) ∧ lf(m0) ≠ [], ∀ n, a. nextl(n, a) ≠ [] ⊦ m = n0 + 1, m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
[] = nextl(m0, lf(m0).last), lf(m0 + 1) = [], lf(0) = a ', m0 < n0, ∀ n, a. nextl(n, a) ≠ [] ⊦ lf(m0) = [], m0 = n0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ 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)