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