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Proof step 1 from proof injectivity (conclusion)

⊦ encode(m, n) = encode(m0, n0) ↔ m = m0 ∧ n = n0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ encode(m, n) = ((m + n) * (m + n + 1)) / 2 + n
Proof step 3:
⊦ ((m + n) * (m + n + 1)) / 2 + n = encode(m0, n0) ↔ m = m0 ∧ n = n0

Rule argument

spec: nat-pair inst: name: encode-def seq: ⊦ encode(m, n) = ((m + n) * (m + n + 1)) / 2 + n subst: [n, m] → [n, m] flags: rewrite, current

Additional information

Used terms: n, m