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 unknownprop_46d319e806423f3dd208e718ffec9ba385835fad7940dfe5f10e1efe5a189ac9 with
x0,
x1,
x3,
x4,
x5,
x6,
x7,
x8,
x9,
x10,
λ x11 x12 . x2 x12 = x9 (x2 (x3 (x4 (x5 (x6 (x7 (x8 x10))))))) leaving 11 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.
Apply unknownprop_a70534b578015d586aa8a72b37829114d577ac778b073fd6e581372f02ba67c0 with
x0,
x1,
x2,
x9,
x3,
x4,
x5,
x6,
x7,
x8,
x10 leaving 11 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 H9.
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 H10.