Let x0 of type ι → ο be given.

Let x1 of type (ι → ι) → ο be given.

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

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

Let x2 of type ι → ι be given.

Let x3 of type ι → ι be given.

Let x4 of type ι → ι be given.

Let x5 of type ι → ι be given.

Let x6 of type ι → ι be given.

Let x7 of type ι → ι be given.

Let x8 of type ι → ι be given.

Let x9 of type ι → ι be given.

Let x10 of type ι → ι be given.

Let x11 of type ι → ι be given.

Let x12 of type ι → ι be given.

Let x13 of type ι → ι be given.

Let x14 of type ι → ι be given.

Assume H2: x1 x2.

Assume H3: x1 x3.

Assume H4: x1 x4.

Assume H5: x1 x5.

Assume H6: x1 x6.

Assume H7: x1 x7.

Assume H8: x1 x8.

Assume H9: x1 x9.

Assume H10: x1 x10.

Assume H11: x1 x11.

Assume H12: x1 x12.

Assume H13: x1 x13.

Assume H14: x1 x14.

Let x15 of type ι be given.

Assume H15: x0 x15.

Apply unknownprop_b28518e2b47087ec7db607a987a2cdda4df2e443928065dcfcb1da19a6240b8c with x0, x1, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, λ x16 x17 . x2 x17 = x14 (x2 (x3 (x4 (x5 (x6 (x7 (x8 (x9 (x10 (x11 (x12 (x13 x15)))))))))))) leaving 16 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

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.

The subproof is completed by applying H15.

Apply unknownprop_86856dc53557f43006395c497f2d178842a6b138bf2819d1af92de475faaf5a9 with x0, x1, x2, x14, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x15 leaving 16 subgoals.