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Proof step 7 from proof get-mklist-01 (previous step)

m0 + 1 < n, ∀ n, a. m0 < n → mklist(a, n)[m0] = a ⊦ mklist(a, n)[m0 + 1] = a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ x ≠ [] → x[n + 1] = x.tail[n]
Proof step 9:
m0 + 1 < n, ∀ n, a. m0 < n → mklist(a, n)[m0] = a ⊦ mklist(a, n).tail[m0] = a, mklist(a, n) = []

Rule argument

spec: <toplevel> name: get-rec-01 seq: ⊦ x ≠ [] → x[n + 1] = x.tail[n] subst: [n, x] → [m0, mklist(a, n)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mklist(a, m) = [] ↔ m = 0; (s)% ⊦ m < n → n ≠ 0; (s) Used terms: m0, mklist(a, n)