Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ι → ι → ο be given.
Assume H1:
∀ x4 . x3 c4def.. x4 x4.
Assume H2:
∀ x4 x5 x6 x7 x8 . x3 x4 x6 x7 ⟶ x3 x5 x7 x8 ⟶ x3 (6b90c.. x4 x5) x6 x8.
Assume H4:
∀ x4 x5 x6 . x3 x4 x5 x6 ⟶ x3 (a6e19.. x4) x5 (0b8ef.. x6).
Assume H5:
∀ x4 x5 x6 . x3 x4 x5 x6 ⟶ x3 (2fe34.. x4) x5 (6c5f4.. x6).
Assume H8:
∀ x4 x5 x6 x7 x8 . x3 x4 x6 x7 ⟶ x3 x5 x6 x8 ⟶ x3 (f9341.. x4 x5) x6 (cfc98.. x7 x8).
Assume H9:
∀ x4 x5 x6 x7 . x3 x4 x5 x7 ⟶ x3 (1fa6d.. x4) (cfc98.. x5 x6) x7.
Assume H10:
∀ x4 x5 x6 x7 . x3 x4 x6 x7 ⟶ x3 (3a365.. x4) (cfc98.. x5 x6) x7.
Apply H5 with
x0,
x1,
x2.
Apply H0 with
x3 leaving 10 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.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H10.