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Proof step 5 from proof max-snd-nls (previous step)

maxenc(m) + (maxenc(m) * maxenc(m) + maxenc(m)) / 2 < m ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 6:
⊦ (maxenc(m) * (maxenc(m) + 1)) / 2 ≤ m ∧ m < ((maxenc(m) + 1) * (maxenc(m) + 2)) / 2
Proof step 7:
(maxenc(m) * (maxenc(m) + 1)) / 2 ≤ m ∧ m < ((maxenc(m) + 1) * (maxenc(m) + 2)) / 2, maxenc(m) + (maxenc(m) * maxenc(m) + maxenc(m)) / 2 < m ⊦

Rule argument

spec: nat-pair inst: name: max-size seq: ⊦ (maxenc(m) * (maxenc(m) + 1)) / 2 ≤ m ∧ m < ((maxenc(m) + 1) * (maxenc(m) + 2)) / 2 subst: [m] → [m] flags: current, []

Additional information

Used terms: m