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Proof step 5 from proof enc-invert (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ encode(m, n) = ((m + n) * (m + n + 1)) / 2 + n
Proof step 7:
⊦ ( ((maxenc(m) - (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) + (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) * ((maxenc(m) - (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) + (m - (maxenc(m) * (maxenc(m) + 1)) / 2) + 1)) / 2 + (m - (maxenc(m) * (maxenc(m) + 1)) / 2) = m

Rule argument

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

Additional information

Used terms: m - (maxenc(m) * (maxenc(m) + 1)) / 2, maxenc(m) - (m - (maxenc(m) * (maxenc(m) + 1)) / 2)