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Proof step 5 from proof mklist-rmdup-01 (previous step)

∀ a. rmdup(mklist(a, n0)) = a ' ⊦ n0 = 0, rmdup(mklist(a, n0 + 1)) = a '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ n ≠ 0 → mklist(a, n) = mklist(a, n -1) + a '
Proof step 7:
∀ a. rmdup(mklist(a, n0)) = a ' ⊦ n0 + 1 = 0, n0 = 0, rmdup(mklist(a, (n0 + 1)-1) + a ') = a '

Rule argument

spec: <toplevel> name: mk-last-02 seq: ⊦ n ≠ 0 → mklist(a, n) = mklist(a, n -1) + a ' subst: [n, a] → [n0 + 1, a] flags: <all paths>

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 Used terms: n0 + 1, a