obtain ⟨N0, hn0⟩ := he
P : ℕ → Prop
h : ∀ (N : ℕ), P N → ∃ M, N < M ∧ P M
he : ∃ N, P N
⊢ ∀ (N : ℕ), ∃ M, N < M ∧ P M
case intro
P : ℕ → Prop
h : ∀ (N : ℕ), P N → ∃ M, N < M ∧ P M
N0 : ℕ
hn0 : P N0
⊢ ∀ (N : ℕ), ∃ M, N < M ∧ P M