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Proof step 52 from proof nextl-lemma-butlast-nonempty (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 53:
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

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m, m0]

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 0 ≤ m; (s)% ⊦ a ' ≠ []; (s)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m, m0