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Proof step 18 from proof weakmon-lem (previous step)

∀ n. ii(n) ≤ ii(n + 1) ⊦ ∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n), ∃ m. n ≤ ii(m)

User applied rule induction

And obtained the following new goals

Proof step 19:
∀ 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. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n), ∃ m. n ≤ ii(m)

Rule argument

indvar: n wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: n