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 be given.

Assume H0: 762f0.. x4 (bf68c.. x0 x2) x3.

Assume H1: 762f0.. x5 (bf68c.. x1 x2) x3.

Let x6 of type ι → ι → ι → ο be given.

Assume H2: ∀ x7 . 74e69.. x7 ⟶ x6 c4def.. x7 x7.

Assume H3: ∀ x7 x8 x9 x10 x11 . x6 x10 x7 x8 ⟶ x6 x11 x8 x9 ⟶ x6 (6b90c.. x10 x11) x7 x9.

Assume H4: ∀ x7 . 74e69.. x7 ⟶ x6 c9248.. x7 5e331...

Assume H5: ∀ x7 x8 x9 x10 . 74e69.. x9 ⟶ x6 x10 x7 x8 ⟶ x6 (a6e19.. x10) x7 (a3eb9.. x8 x9).

Assume H6: ∀ x7 x8 x9 x10 . 74e69.. x8 ⟶ x6 x10 x7 x9 ⟶ x6 (2fe34.. x10) x7 (a3eb9.. x8 x9).

Assume H7: ∀ x7 x8 x9 x10 x11 x12 . x6 x11 (bf68c.. x7 x9) x10 ⟶ x6 x12 (bf68c.. x8 x9) x10 ⟶ x6 (3e00e.. x11 x12) (bf68c.. (a3eb9.. x7 x8) x9) x10.

Assume H8: ∀ x7 x8 x9 x10 x11 . x6 x10 x7 x8 ⟶ x6 x11 x7 x9 ⟶ x6 (f9341.. x10 x11) x7 (bf68c.. x8 x9).

Assume H9: ∀ x7 x8 x9 x10 . 74e69.. x8 ⟶ x6 x10 x7 x9 ⟶ x6 (1fa6d.. x10) (bf68c.. x7 x8) x9.

Assume H10: ∀ x7 x8 x9 x10 . 74e69.. x7 ⟶ x6 x10 x8 x9 ⟶ x6 (3a365.. x10) (bf68c.. x7 x8) x9.

Apply H7 with x0, x1, x2, x3, x4, x5 leaving 2 subgoals.

Apply H0 with x6 leaving 9 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.

Apply H1 with x6 leaving 9 subgoals.