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.

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.

Apply unknownprop_0e97487862cce1477fe8da74f93de660761987d23f188fc8df231ce3db9e9641 with x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, λ x14 x15 . x15 = x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x2 (x1 x3 (x1 x4 (x1 x5 x13)))))))))) leaving 15 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.

Apply unknownprop_dbc71d98a035c8306d57233ef43ac1dc1c3595d3ca96bfb567b2f45226c0dc37 with x0, x1, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x2, x13 leaving 14 subgoals.