Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply H0 with
λ x3 . x3 = pack_e_e x0 x1 x2 ⟶ x1 ∈ x0 leaving 2 subgoals.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H1: x4 ∈ x3.
Let x5 of type ι be given.
Assume H2: x5 ∈ x3.
Apply pack_e_e_inj with
x3,
x0,
x4,
x1,
x5,
x2,
x1 ∈ x0 leaving 2 subgoals.
The subproof is completed by applying H3.
Assume H4:
and (x3 = x0) (x4 = x1).
Apply H4 with
x5 = x2 ⟶ x1 ∈ x0.
Assume H5: x3 = x0.
Assume H6: x4 = x1.
Assume H7: x5 = x2.
Apply H5 with
λ x6 x7 . x1 ∈ x6.
Apply H6 with
λ x6 x7 . x6 ∈ x3.
The subproof is completed by applying H1.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H1.