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Proof step 3 from proof dec-nat (previous step)

¬ n % 2 ≠ 0 ⊦ decode(encode(n)) = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n % 2 = 0 ⊦ decode(n→i(n / 2)) = n

Rule argument

Additional information

Used simplifier rules: enc-nat-pos: ⊦ n % 2 = 0 → encode(n) = n→i(n / 2);