Let x0 of type ι → ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type (ι → ο) → ι → ι → ο be given.
Assume H3:
∀ x5 : ι → ο . ∀ x6 x7 : ι → ι . (∀ x8 . x4 (de327.. x5 x8) (x6 x8) (x7 x8)) ⟶ x4 x5 (56103.. x6) (56103.. x7).
Assume H4:
∀ x5 : ι → ο . ∀ x6 x7 x8 . x4 x5 x6 x8 ⟶ 707bb.. x5 x7 ⟶ x4 x5 (57d6a.. x6 x7) (57d6a.. x8 x7).
Assume H5:
∀ x5 : ι → ο . ∀ x6 x7 x8 . x4 x5 x7 x8 ⟶ 707bb.. x5 x6 ⟶ x4 x5 (57d6a.. x6 x7) (57d6a.. x6 x8).
Apply H4 with
x0,
x1,
x2,
x3 leaving 2 subgoals.
Apply H0 with
x4 leaving 4 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H1.