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Proof step 21 from proof weakmon-lem (previous step)

∀ n. ii(n) ≤ ii(n + 1), ∀ n0, ii. n0 < n → (∀ n. ii(n) ≤ ii(n + 1)) → (∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n)) ∨ (∃ m. n0 ≤ ii(m)) ⊦ n = 0, ∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n), ∃ m. n ≤ ii(m)

User applied rule exists right

And obtained the following new goals

Proof step 22:
∀ n. ii(n) ≤ ii(n + 1), ∀ n0, ii. n0 < n → (∀ n. ii(n) ≤ ii(n + 1)) → (∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n)) ∨ (∃ m. n0 ≤ ii(m)) ⊦ n = 0, ∃ m. n ≤ ii(m), ∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n), (∀ m. ii(m) ≤ n - 1) ∧ (∃ m. ii(m) = n - 1)

Rule argument

pos: right 2 terms: n - 1 abort: F discard: F computed: F

Additional information

Used terms: n - 1