Let x0 of type ι → ο be given.

Let x1 of type ι → ι → ι be given.

Assume H0: ∀ x2 x3 . x0 x2 ⟶ x0 x3 ⟶ x0 (x1 x2 x3).

Assume H1: ∀ x2 x3 x4 . x0 x2 ⟶ x0 x3 ⟶ x0 x4 ⟶ x1 x2 (x1 x3 x4) = x1 x3 (x1 x2 x4).

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.

Let x6 of type ι be given.

Let x7 of type ι be given.

Let x8 of type ι be given.

Let x9 of type ι be given.

Let x10 of type ι be given.

Let x11 of type ι be given.

Assume H2: x0 x2.

Assume H3: x0 x3.

Assume H4: x0 x4.

Assume H5: x0 x5.

Assume H6: x0 x6.

Assume H7: x0 x7.

Assume H8: x0 x8.

Assume H9: x0 x9.

Assume H10: x0 x10.

Assume H11: x0 x11.

Apply unknownprop_57b72403a262e58313ce568ea812ef6d89ec67b4e1a215ab6f60d964bf3d2756 with x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, λ x12 x13 . x13 = x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x2 (x1 x3 (x1 x4 (x1 x5 x11)))))))) leaving 13 subgoals.

The subproof is completed by applying H0.

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.

The subproof is completed by applying H11.

Apply unknownprop_4402c4add48ff346491c84f79be39dee9e90d48d41f25c112bf586ab9bf76ce5 with x0, x1, x3, x4, x5, x6, x7, x8, x9, x10, x2, x11 leaving 12 subgoals.