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 → ι be given.
Assume H2: ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ x3 x4 x5 ∈ x0.
Let x4 of type ι → ο be given.
Assume H3:
∀ x5 . ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ x5 ⟶ ∀ x8 . x8 ∈ x5 ⟶ x6 x7 x8 ∈ x5) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . x8 ∈ x5 ⟶ ∀ x9 . x9 ∈ x5 ⟶ x7 x8 x9 ∈ x5) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . x9 ∈ x5 ⟶ ∀ x10 . x10 ∈ x5 ⟶ x8 x9 x10 ∈ x5) ⟶ x4 (pack_b_b_b x5 x6 x7 x8).
Apply H3 with
x0,
x1,
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.