c : Cardinal
h : ℵ₀ ≤ c
⊢ ω ≤ ord c
c : Cardinal
h : ℵ₀ ≤ c
⊢ c + 1 = c
rw [add_comm, ← card_ord c, ← card_one, ← card_add, one_add_of_omega_le]
no goals
c : Cardinal
h : ℵ₀ ≤ c
⊢ ω ≤ ord c
rwa [← ord_aleph0, ord_le_ord]