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Proof step 19 from proof max-def (previous step)

m < ((m0 + 1) * (m0 + 2)) / 2, m < ((m0 + 1) * (m0 + 2)) / 2, true, ∀ m2, m3, n. m2 - m3 < m - m0 → true → (n * (n + 1)) / 2 ≤ m2 ∧ m2 < ((n + 1) * (n + 2)) / 2 ∧ (m3 * (m3 + 1)) / 2 ≤ m2 → maxenc(m3, m2) = n ⊦ (m0 * (m0 + 1)) / 2 ≤ (n * (n + 1)) / 2 + 0 ∧ (n * (n + 1)) / 2 + 0 < ((m0 + 1) * (m0 + 2)) / 2 ∧ 0 ≤ n, ¬ m0 < n, (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → m0 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ n + 0 = n
Proof step 21:
m < ((m0 + 1) * (m0 + 2)) / 2, m < ((m0 + 1) * (m0 + 2)) / 2, true, ∀ m2, m3, n. m2 - m3 < m - m0 → true → (n * (n + 1)) / 2 ≤ m2 ∧ m2 < ((n + 1) * (n + 2)) / 2 ∧ (m3 * (m3 + 1)) / 2 ≤ m2 → maxenc(m3, m2) = n ⊦ (m0 * (m0 + 1)) / 2 ≤ (n * (n + 1)) / 2 ∧ (n * (n + 1)) / 2 < ((m0 + 1) * (m0 + 2)) / 2 ∧ 0 ≤ n, ¬ m0 < n, (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → m0 = n

Rule argument

spec: nat-basic2 inst: name: add-base seq: ⊦ n + 0 = n subst: [n] → [(n * (n + 1)) / 2] flags: rewrite

Additional information

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