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.

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.

Let x14 of type ι be given.

Assume H14: x0 x14.

Apply unknownprop_71fd44a88b6517c6e2eab9ece368aa2cf87e4b657522ab1b9bac0c163646ef49 with x0, x1, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, λ x15 x16 . x2 x16 = x13 (x2 (x3 (x4 (x5 (x6 (x7 (x8 (x9 (x10 (x11 (x12 x14))))))))))) leaving 15 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.

Apply unknownprop_1ffc9071a1eb892280fc9b428d18d0cbca1f67de9a2954bc0c3ef11a987ec602 with x0, x1, x2, x13, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x14 leaving 15 subgoals.