Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H2: x1 ∈ x0.
Let x2 of type ι be given.
Assume H4:
∀ x3 . x3 ∈ x1 ⟶ ap x2 x3 ∈ x0.
Apply unknownprop_214e605da056dadef5daf9b0d158a4ef0cf22c6dec72467d2b450a0dea764590 with
x1,
x2,
λ x3 x4 . x4 ∈ x0 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_d9ae82204b18e6cf15c85d865639887282bf3ebbe7f609859927820b6a09adb1 with
x0,
x1,
λ x3 . ap x2 x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H4.