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Proof step 10 from proof get-mklist-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ≠ 0 → mklist(a, n).tail = mklist(a, n -1)
Proof step 12:
m0 + 1 < n, ∀ n, a. m0 < n → mklist(a, n)[m0] = a ⊦ mklist(a, n -1)[m0] = a, n = 0

Rule argument

spec: list-last name: mk-tail seq: ⊦ n ≠ 0 → mklist(a, n).tail = mklist(a, n -1) subst: [n, a] → [n, a] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mklist(a, 0) = []; (s)%n0 < n ⊦ ¬ m + (* n) < (* n0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n, a