Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2.
Let x2 of type ο be given.
Assume H4:
∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ 91306.. x1 x3 x4 x5 x6 ⟶ x2.
Assume H5:
∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ 65a4c.. x1 x3 x4 x5 x6 ⟶ x2.
Assume H6:
∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ a1d37.. x1 x3 x4 x5 x6 ⟶ x2.
Apply unknownprop_467135a8a9aef5db3cbe1368b65a9d4158cef0a1c35752402f3d2165ccb616b1 with
x0,
x1,
x2 leaving 10 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 L9.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Let x3 of type ι be given.
Assume H10: x3 ∈ x0.
Let x4 of type ι be given.
Assume H11: x4 ∈ x0.
Let x5 of type ι be given.
Assume H12: x5 ∈ x0.
Let x6 of type ι be given.
Assume H13: x6 ∈ x0.
Assume H14:
2f869.. x1 x3 x4 x5 x6.
Apply H14 with
x2.
Assume H15: x3 = x4 ⟶ ∀ x7 : ο . x7.
Assume H16: x3 = x5 ⟶ ∀ x7 : ο . x7.
Assume H17: x4 = x5 ⟶ ∀ x7 : ο . x7.
Assume H18: x3 = x6 ⟶ ∀ x7 : ο . x7.
Assume H19: x4 = x6 ⟶ ∀ x7 : ο . x7.
Assume H20: x5 = x6 ⟶ ∀ x7 : ο . x7.
Assume H21:
not (x1 x3 x4).
Assume H22:
not (x1 x3 x5).
Assume H23:
not (x1 x4 x5).
Assume H24:
not (x1 x3 x6).
Assume H25:
not (x1 x4 x6).
Assume H26: x1 x5 x6.
Apply FalseE with
x2.
Apply L8 with
x3,
x4,
x5 leaving 9 subgoals.
The subproof is completed by applying H10.
The subproof is completed by applying H11.
The subproof is completed by applying H12.
The subproof is completed by applying H15.
The subproof is completed by applying H16.
The subproof is completed by applying H17.
The subproof is completed by applying H21.
The subproof is completed by applying H22.
The subproof is completed by applying H23.
The subproof is completed by applying H6.
Let x3 of type ι be given.
Assume H10: x3 ∈ x0.
Let x4 of type ι be given.
Assume H11: x4 ∈ x0.
Let x5 of type ι be given.
Assume H12: x5 ∈ x0.
Let x6 of type ι be given.
Assume H13: x6 ∈ x0.
Assume H14:
180f5.. x1 x3 x4 x5 x6.
Apply H14 with
x2.
Assume H15: x3 = x4 ⟶ ∀ x7 : ο . x7.
Assume H16: x3 = x5 ⟶ ∀ x7 : ο . x7.
Assume H17: x4 = x5 ⟶ ∀ x7 : ο . x7.
Assume H18: x3 = x6 ⟶ ∀ x7 : ο . x7.
Assume H19: x4 = x6 ⟶ ∀ x7 : ο . x7.
Assume H20: x5 = x6 ⟶ ∀ x7 : ο . x7.
Assume H21:
not (x1 x3 x4).
Assume H22:
not (x1 x3 ...).