Let x0 of type ι → ο be given.
Let x1 of type ι → ι → ο be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: x1 x2 x3.
Let x4 of type ι → ι → ο be given.
Assume H1: ∀ x5 x6 . x1 x5 x6 ⟶ x4 x5 x6.
Assume H2: ∀ x5 . x0 x5 ⟶ x4 x5 x5.
Assume H3: ∀ x5 x6 . x4 x5 x6 ⟶ x4 x6 x5.
Assume H4: ∀ x5 x6 x7 . x4 x5 x6 ⟶ x4 x6 x7 ⟶ x4 x5 x7.
Apply H1 with
x2,
x3.
The subproof is completed by applying H0.