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 be given.
Let x4 of type ι be given.
Let x5 of type ι → ι → ι → ο be given.
Assume H2:
∀ x6 . x5 c4def.. x6 x6.
Assume H3:
∀ x6 x7 x8 x9 x10 . x5 x6 x8 x9 ⟶ x5 x7 x9 x10 ⟶ x5 (6b90c.. x6 x7) x8 x10.
Assume H5:
∀ x6 x7 x8 . x5 x6 x7 x8 ⟶ x5 (a6e19.. x6) x7 (0b8ef.. x8).
Assume H6:
∀ x6 x7 x8 . x5 x6 x7 x8 ⟶ x5 (2fe34.. x6) x7 (6c5f4.. x8).
Assume H9:
∀ x6 x7 x8 x9 x10 . x5 x6 x8 x9 ⟶ x5 x7 x8 x10 ⟶ x5 (f9341.. x6 x7) x8 (cfc98.. x9 x10).
Assume H10:
∀ x6 x7 x8 x9 . x5 x6 x7 x9 ⟶ x5 (1fa6d.. x6) (cfc98.. x7 x8) x9.
Assume H11:
∀ x6 x7 x8 x9 . x5 x6 x8 x9 ⟶ x5 (3a365.. x6) (cfc98.. x7 x8) x9.
Apply H8 with
x0,
x1,
x2,
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H1 with
x5 leaving 10 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 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.
The subproof is completed by applying H11.