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Proof step 3 from proof snd-def (previous step)

⊦ encode(m, n) - (maxenc(encode(m, n)) * (maxenc(encode(m, n)) + 1)) / 2 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ encode(m, n) = ((m + n) * (m + n + 1)) / 2 + n
Proof step 5:
⊦ ((m + n) * (m + n + 1)) / 2 + n - (maxenc(((m + n) * (m + n + 1)) / 2 + n) * (maxenc(((m + n) * (m + n + 1)) / 2 + n) + 1)) / 2 = n

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