Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Apply unpack_u_i_eq with
(λ x5 x6 x7 . λ x8 : ι → ι . pack_u {x9 ∈ x7|ap x5 x9 = ap x6 x9} x8) x3 x4,
x0,
x1.
Let x5 of type ι → ι be given.
Assume H0: ∀ x6 . x6 ∈ x0 ⟶ x1 x6 = x5 x6.
Apply pack_u_ext with
{x6 ∈ x0|ap x3 x6 = ap x4 x6},
x5,
x1.
Let x6 of type ι be given.
Assume H1:
x6 ∈ {x7 ∈ x0|ap x3 x7 = ap x4 x7}.
Let x7 of type ι → ι → ο be given.
Apply H0 with
x6,
λ x8 x9 . x7 x9 x8.
Apply SepE1 with
x0,
λ x8 . ap x3 x8 = ap x4 x8,
x6.
The subproof is completed by applying H1.