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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%succ-01: ⊦ m + 1 ≤ n ↔ m < n; from specification nat%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2