Let x0 of type ι → ι → ο be given.
Let x1 of type ι → ι → ο be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type (ι → ι → ο) → ι → ι → ο be given.
Assume H5: ∀ x9 : ι → ι → ο . ∀ x10 x11 . x0 x10 x11 ⟶ x8 x9 x10 x11.
Assume H6: ∀ x9 : ι → ι → ο . ∀ x10 x11 . x9 x10 x11 ⟶ x8 x9 x10 x11.
Assume H8:
∀ x9 : ι → ι → ο . ∀ x10 x11 . ∀ x12 : ι → ι . f6435.. x10 ⟶ x8 x9 x11 32d20.. ⟶ (∀ x13 . x8 (a603a.. x9 x13 x11) (x12 x13) x10) ⟶ x8 x9 (d7cf0.. x11 x12) x10.
Assume H9:
∀ x9 : ι → ι → ο . ∀ x10 x11 x12 . ∀ x13 : ι → ι . x8 x9 x10 (d7cf0.. x12 x13) ⟶ x8 x9 x11 x12 ⟶ x8 x9 (57d6a.. x10 x11) (x13 x11).
Assume H11:
∀ x9 : ι → ι → ο . ∀ x10 x11 . ∀ x12 x13 : ι → ι . f6435.. x10 ⟶ x8 x9 (d7cf0.. x11 x13) x10 ⟶ (∀ x14 . x8 (a603a.. x9 x14 x11) (x12 x14) (x13 x14)) ⟶ x8 x9 (bcddf.. x11 x12) (d7cf0.. x11 x13).
Assume H12:
∀ x9 : ι → ι → ο . ∀ x10 x11 x12 x13 x14 . f6435.. x10 ⟶ x8 x9 x11 x12 ⟶ x8 x9 x13 x10 ⟶ d3ec1.. x1 x12 x14 ⟶ d3ec1.. x1 x13 x14 ⟶ x8 x9 x11 x13.
Apply H12 with
x2,
x3,
x4,
x5,
x6,
x7 leaving 5 subgoals.
The subproof is completed by applying H0.
Apply H1 with
x8 leaving 8 subgoals.
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.
The subproof is completed by applying H12.
Apply H2 with
x8 leaving 8 subgoals.
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.
The subproof is completed by applying H12.
The subproof is completed by applying H3.
The subproof is completed by applying H4.