Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ x1 x2 ∈ x0.
Assume H1: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 = x1 x3 ⟶ x2 = x3.
Apply andI with
struct_u (pack_u x0 x1),
unpack_u_o (pack_u x0 x1) (λ x2 . λ x3 : ι → ι . inj x2 x2 (λ x4 . x3 x4)) leaving 2 subgoals.
Apply pack_struct_u_I with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_a16c1e4668d0beb05131d186b11d5f445a514d4e4db3d676d988ae675bef6e8e with
x0,
x1,
λ x2 x3 : ο . x3.
Apply andI with
∀ x2 . x2 ∈ x0 ⟶ x1 x2 ∈ x0,
∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 = x1 x3 ⟶ x2 = x3 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.