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Proof step 1 from proof dec-nat (conclusion)

⊦ decode(encode(n)) = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ n % 2 ≠ 0 → encode(n) = ~ n→i((n + 1) / 2)
Proof step 3:
¬ n % 2 ≠ 0 ⊦ decode(encode(n)) = n
Proof step 6:
n % 2 ≠ 0 ⊦ decode(~ n→i((n + 1) / 2)) = n

Rule argument

spec: int-pair inst: name: enc-nat-neg seq: ⊦ n % 2 ≠ 0 → encode(n) = ~ n→i((n + 1) / 2) subst: [n] → [n] flags: rewrite, current

Additional information

Used terms: n