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.

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.

Let x13 of type ι be given.

Assume H13: x0 x13.

Apply unknownprop_2bb7e2b8b1d6c03f5ec8d3310acff393b6f23d539a10a09170ab6ce8840032f3 with x0, x1, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, λ x14 x15 . x2 x15 = x12 (x2 (x3 (x4 (x5 (x6 (x7 (x8 (x9 (x10 (x11 x13)))))))))) leaving 14 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.

Apply unknownprop_49730781d2cd8e079c94e39f886b1363640d9d7a8c2850c05d4ec426ef0bdc83 with x0, x1, x2, x12, x3, x4, x5, x6, x7, x8, x9, x10, x11, x13 leaving 14 subgoals.