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Proof step 1 from proof max-rev (conclusion)

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

User applied rule induction

And obtained the following new goals

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

Rule argument

indvar: m - m0 wfpred: <

Additional information

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