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.
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.
Let x10 of type ι be given.
Assume H10: x0 x10.
Apply H1 with
x2,
x3,
x4 (x5 (x6 (x7 (x8 (x9 x10))))) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_9df0051fe5649d34dd14e90f9946f82bcfe3445ae6c6fefd9c7d30607b4a3534 with
x0,
x1,
x9,
x8,
x7,
x6,
x5,
x4,
x10 leaving 8 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H9.
The subproof is completed by applying H8.
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 H10.