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Proof step 5 from proof max-rev (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → maxenc(m0, m) = n
Proof step 7:
maxenc(m0, m) = n, (m0 * (m0 + 1)) / 2 ≤ m, ∀ m2, m3, n. m2 - m3 < m - m0 → maxenc(m3, m2) = n ∧ (m3 * (m3 + 1)) / 2 ≤ m2 → (n * (n + 1)) / 2 ≤ m2 ∧ m2 < ((n + 1) * (n + 2)) / 2 ⊦ ((m0 + 1) * (m0 + 2)) / 2 ≤ m, (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2, (m0 * (m0 + 1)) / 2 ≤ m ∧ m < ((m0 + 1) * (m0 + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m

Rule argument

spec: <toplevel> name: max-def seq: ⊦ (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → maxenc(m0, m) = n subst: [n, m, m0] → [m0, m, m0] flags: <all paths>

Additional information

Used terms: m0, m, m0