Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
λ x2 . struct_b (3d151.. x2 x1).
Let x2 of type ι be given.
Let x3 of type ι → ι → ι be given.
Assume H2: ∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ x3 x4 x5 ∈ x2.
Apply H1 with
λ x4 . struct_b (3d151.. (pack_b x2 x3) x4).
Let x4 of type ι be given.
Let x5 of type ι → ι → ι be given.
Assume H3: ∀ x6 . x6 ∈ x4 ⟶ ∀ x7 . x7 ∈ x4 ⟶ x5 x6 x7 ∈ x4.
Apply unknownprop_84b7a40932bac82c3ecf4fa49a1bea60dc509b45bddc18bf9510d8d39709513f with
x2,
x3,
x4,
x5,
λ x6 x7 . struct_b x7.
Apply pack_struct_b_I with
setprod x2 x4,
λ x6 x7 . lam 2 (λ x8 . If_i (x8 = 0) (x3 (ap x6 0) (ap x7 0)) (x5 (ap x6 1) (ap x7 1))).
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply tuple_2_Sigma with
x2,
λ x8 . x4,
x3 (ap x6 0) (ap x7 0),
x5 (ap x6 1) (ap x7 1) leaving 2 subgoals.
Apply H2 with
ap x6 0,
ap x7 0 leaving 2 subgoals.
Apply ap0_Sigma with
x2,
λ x8 . x4,
x6.
The subproof is completed by applying H4.
Apply ap0_Sigma with
x2,
λ x8 . x4,
x7.
The subproof is completed by applying H5.
Apply H3 with
ap x6 1,
ap x7 1 leaving 2 subgoals.
Apply ap1_Sigma with
x2,
λ x8 . x4,
x6.
The subproof is completed by applying H4.
Apply ap1_Sigma with
x2,
λ x8 . x4,
x7.
The subproof is completed by applying H5.