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Proof step 7 from proof fst-def (previous step)

⊦ m + n - (((m + n) * (m + n + 1)) / 2 + n).2 = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ m.2 = m - (maxenc(m) * (maxenc(m) + 1)) / 2
Proof step 9:
⊦ m + n - (((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) = m

Rule argument

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

Additional information

Used terms: ((m + n) * (m + n + 1)) / 2 + n