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.

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.

Let x11 of type ι be given.

Assume H11: x0 x11.

Apply unknownprop_21c06cce548a4df9c9e16000463af5090a8e642f7e7cc473868276ae6a47442e with x0, x1, x3, x4, x5, x6, x7, x8, x9, x10, x11, λ x12 x13 . x2 x13 = x10 (x2 (x3 (x4 (x5 (x6 (x7 (x8 (x9 x11)))))))) leaving 12 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.

Apply unknownprop_b1aaba33db17a303ddb30941ee77351426bfd4f0c7e33f15d2b477db9de4e3f2 with x0, x1, x2, x10, x3, x4, x5, x6, x7, x8, x9, x11 leaving 12 subgoals.