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Proof step 4 from proof dec-nat (previous step)

n % 2 = 0 ⊦ decode(n→i(n / 2)) = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ i → decode(i) = 2 * i→n(i)
Proof step 6:
n % 2 = 0, 0 ≤ n→i(n / 2) ⊦ 2 * i→n(n→i(n / 2)) = n

Rule argument

spec: <toplevel> name: dec-nat-pos seq: ⊦ 0 ≤ i → decode(i) = 2 * i→n(i) subst: [i] → [n→i(n / 2)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n); (s) Used terms: n→i(n / 2)