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Proof step 6 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 7:
⊦ x ≠ [] → x[n + 1] = x.rest[n]
Proof step 8:
mklist(a, n) ≠ [], m0 + 1 < n, ∀ n, a. m0 < n → mklist(a, n)[m0] = a ⊦ mklist(a, n).rest[m0] = a

Rule argument

spec: list-del inst: name: get-rec-01 seq: ⊦ x ≠ [] → x[n + 1] = x.rest[n] subst: [n, x] → [m0, mklist(a, n)] flags: rewrite, current

Additional information

Used simplifier rules: mk-empty: ⊦ mklist(a, m) = [] ↔ m = 0; from specification list-last%f: ⊦ m < n → n ≠ 0; from specification nat-basic1 Used terms: m0, mklist(a, n)