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.

Let x12 of type ι be given.

Let x13 of type ι be given.

Let x14 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.

Assume H12: x0 x12.

Assume H13: x0 x13.

Assume H14: x0 x14.

Apply unknownprop_11e965f93428511be41c648b44c7042f42623600fd53ca75488c6932c5d19c48 with x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, λ x15 x16 . x16 = x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x2 (x1 x3 (x1 x4 x14))))))))))) leaving 16 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.

The subproof is completed by applying H12.

The subproof is completed by applying H13.

The subproof is completed by applying H14.

Apply unknownprop_83088b7db1e7e6e9f784934953b5360c364bc32df2307f7e01a5e58240db59f8 with x0, x1, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x2, x14 leaving 15 subgoals.