Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
λ x2 . struct_u (5a1fb.. x2 x1).
Let x2 of type ι be given.
Let x3 of type ι → ι be given.
Assume H2: ∀ x4 . x4 ∈ x2 ⟶ x3 x4 ∈ x2.
Apply H1 with
λ x4 . struct_u (5a1fb.. (pack_u x2 x3) x4).
Let x4 of type ι be given.
Let x5 of type ι → ι be given.
Assume H3: ∀ x6 . x6 ∈ x4 ⟶ x5 x6 ∈ x4.
Apply unknownprop_d4e4b2b932101a362c6dcbb7a861a9344a66a83ebdf6fb8c344e912c8c3c1d9a with
x2,
x3,
x4,
x5,
λ x6 x7 . struct_u x7.
Apply pack_struct_u_I with
setprod x2 x4,
λ x6 . lam 2 (λ x7 . If_i (x7 = 0) (x3 (ap x6 0)) (x5 (ap x6 1))).
Let x6 of type ι be given.
Apply tuple_2_Sigma with
x2,
λ x7 . x4,
x3 (ap x6 0),
x5 (ap x6 1) leaving 2 subgoals.
Apply H2 with
ap x6 0.
Apply ap0_Sigma with
x2,
λ x7 . x4,
x6.
The subproof is completed by applying H4.
Apply H3 with
ap x6 1.
Apply ap1_Sigma with
x2,
λ x7 . x4,
x6.
The subproof is completed by applying H4.