Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: 0 ∈ x3.
Assume H1: x2 ⊆ x3.
Assume H2: x0 ⊆ x1.
Apply Pi_0_mon with
x0,
x1,
λ x4 . x2,
λ x4 . x3 leaving 3 subgoals.
Let x4 of type ι be given.
Assume H3: x4 ∈ x0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Let x4 of type ι be given.
Assume H3: x4 ∈ x1.
The subproof is completed by applying H0.