Proofgold Proof

pf
Apply andI with TransSet omega, ∀ x0 . x0 ∈ omega ⟶ TransSet x0 leaving 2 subgoals. The subproof is completed by applying omega_TransSet. Let x0 of type ι be given. Assume H0: x0 ∈ omega. Apply ordinal_TransSet with x0. Apply nat_p_ordinal with x0. Apply omega_nat_p with x0. The subproof is completed by applying H0. ■