True ↔ ∀ {V : Type u_1} (G : SimpleGraph V), G.chromaticCardinal = Cardinal.aleph 1 → ∃ EColor, ∃ (_ : Cardinal.mk EColor = Cardinal.aleph 1), ∃ c_edge, ∀ (VColor : Type), Cardinal.mk VColor ≤ Cardinal.aleph 0 → ∀ (c_vert : V → VColor), ∃ vc, ∀ (ec : EColor), ∃ u v, ∃ (h : G.Adj u v), c_vert u = vc ∧ c_vert v = vc ∧ c_edge ⟨s(u, v), h⟩ = ec