Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Apply H0 with
λ x2 . x2 = pack_u x0 x1 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x3 ∈ x0 leaving 2 subgoals.
Let x2 of type ι be given.
Let x3 of type ι → ι be given.
Assume H1: ∀ x4 . x4 ∈ x2 ⟶ x3 x4 ∈ x2.
Apply pack_u_inj with
x2,
x0,
x3,
x1,
∀ x4 . x4 ∈ x0 ⟶ x1 x4 ∈ x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: x2 = x0.
Assume H4: ∀ x4 . x4 ∈ x2 ⟶ x3 x4 = x1 x4.
Apply H3 with
λ x4 x5 . ∀ x6 . x6 ∈ x4 ⟶ x1 x6 ∈ x4.
Let x4 of type ι be given.
Assume H5: x4 ∈ x2.
Apply H4 with
x4,
λ x5 x6 . x5 ∈ x2 leaving 2 subgoals.
The subproof is completed by applying H5.
Apply H1 with
x4.
The subproof is completed by applying H5.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H1.