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).
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 H1: x1 x2.
Assume H2: x1 x3.
Assume H3: x1 x4.
Assume H4: x1 x5.
Assume H5: x1 x6.
Assume H6: x1 x7.
Assume H7: x1 x8.
Assume H8: x1 x9.
Let x10 of type ι be given.
Assume H9: x0 x10.
Apply H0 with
x9,
x8 (x7 (x6 (x5 (x4 (x3 (x2 x10)))))) leaving 2 subgoals.
The subproof is completed by applying H8.
Apply unknownprop_f9dac9dcb632653e5daff02aecdc1b2454f714ec934721e932ed39cedb936920 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
x10 leaving 9 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
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 H9.