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.
Assume H2: x1 x2.
Assume H3: x1 x3.
Assume H4: x1 x4.
Assume H5: x1 x5.
Assume H6: x1 x6.
Assume H7: x1 x7.
Let x8 of type ι be given.
Assume H8: x0 x8.
Apply H1 with
x2,
x3,
x4 (x5 (x6 (x7 x8))) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_ab41805a8a4ab7c7c01a1df079c60a640aa70314c21617f5f9dfae767cc5368c with
x0,
x1,
x7,
x6,
x5,
x4,
x8 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H7.
The subproof is completed by applying H6.
The subproof is completed by applying H5.
The subproof is completed by applying H4.
The subproof is completed by applying H8.