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 → ο) → ι → ο be given.
Assume H2: ∀ x4 : ι → ο . ∀ x5 . x4 x5 ⟶ x3 x4 x5.
Assume H3:
∀ x4 : ι → ο . ∀ x5 : ι → ι . (∀ x6 . x3 (de327.. x4 x6) (x5 x6)) ⟶ x3 x4 (56103.. x5).
Assume H4:
∀ x4 : ι → ο . ∀ x5 x6 . x3 x4 x5 ⟶ x3 x4 x6 ⟶ x3 x4 (57d6a.. x5 x6).
Apply H4 with
x0,
x1,
x2 leaving 2 subgoals.
Apply H0 with
x3 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply H1 with
x3 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.