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.
Assume H1: x1 x2.
Assume H2: x1 x3.
Assume H3: x1 x4.
Assume H4: x1 x5.
Assume H5: x1 x6.
Assume H6: x1 x7.
Let x8 of type ι be given.
Assume H7: x0 x8.
Apply H0 with
x7,
x6 (x5 (x4 (x3 (x2 x8)))) leaving 2 subgoals.
The subproof is completed by applying H6.
Apply unknownprop_f50d30ec41a9ed1eb36047ef858083f2c1ecab3e502982a12fc1b061c8d0fdfb with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x8 leaving 7 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 H7.