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Proof step 2 from proof max-def (previous step)

m < ((n + 1) * (n + 2)) / 2, (n * (n + 1)) / 2 ≤ m, (m0 * (m0 + 1)) / 2 ≤ m ⊦ maxenc(m0, m) = n

User applied rule induction

And obtained the following new goals

Proof step 3:
m < ((n + 1) * (n + 2)) / 2, (n * (n + 1)) / 2 ≤ m, (m0 * (m0 + 1)) / 2 ≤ m, ∀ m2, m3, n. m2 - m3 < m - m0 → m2 < ((n + 1) * (n + 2)) / 2 ∧ (n * (n + 1)) / 2 ≤ m2 ∧ (m3 * (m3 + 1)) / 2 ≤ m2 → maxenc(m3, m2) = n ⊦ maxenc(m0, m) = n

Rule argument

indvar: m - m0 wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: m - m0