Let x0 of type ι be given.
Assume H0: 0 ∈ x0.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H2: x2 ∈ x1.
Apply setexp_0_dom_mon with
x0,
x2,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply nat_trans with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.