Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H1: x1 ∈ x0.
Apply nat_p_omega with
x1.
Apply nat_p_trans with
x0,
x1 leaving 2 subgoals.
Apply omega_nat_p with
x0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.