Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0:
∀ x2 . x2 ∈ x0 ⟶ not (x1 x2 x2).
Assume H1: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2.
Apply andI with
struct_r (pack_r x0 x1),
unpack_r_o (pack_r x0 x1) (λ x2 . λ x3 : ι → ι → ο . and (∀ x4 . x4 ∈ x2 ⟶ not (x3 x4 x4)) (∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ x3 x4 x5 ⟶ x3 x5 x4)) leaving 2 subgoals.
The subproof is completed by applying pack_struct_r_I with x0, x1.
Apply unknownprop_ee6d5f0119c23d2d365410bede08f376d1ae2b56e8e57cf05f64e993f9b9e31e with
x0,
x1,
λ x2 x3 : ο . x3.
Apply andI with
∀ x2 . x2 ∈ x0 ⟶ not (x1 x2 x2),
∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.