Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ∈ x0.
Let x2 of type ι → ι → ι be given.
Assume H1: ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x2 x3 x4 ∈ x0.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι be given.
Assume H2: x4 ∈ x0.
Let x5 of type ι be given.
Assume H3: x5 ∈ x0.
Let x6 of type ι → ο be given.
Assume H4:
∀ x7 . ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ x7 ⟶ ∀ x10 . x10 ∈ x7 ⟶ x8 x9 x10 ∈ x7) ⟶ ∀ x9 : ι → ι → ι . (∀ x10 . x10 ∈ x7 ⟶ ∀ x11 . x11 ∈ x7 ⟶ x9 x10 x11 ∈ x7) ⟶ ∀ x10 : ι → ι → ο . ∀ x11 . x11 ∈ x7 ⟶ ∀ x12 . x12 ∈ x7 ⟶ x6 (pack_b_b_r_e_e x7 x8 x9 x10 x11 x12).
Apply H4 with
x0,
x1,
x2,
x3,
x4,
x5 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.