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 ⟶ 9518f.. x1 x3 x4 x5 ⟶ x2.
Assume H5:
∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ 67a24.. x1 x3 x4 x5 ⟶ x2.
Claim L6:
∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ not (x1 x3 x4) ⟶ not (x1 x4 x3)Let x3 of type ι be given.
Assume H6: x3 ∈ x0.
Let x4 of type ι be given.
Assume H7: x4 ∈ x0.
Assume H8:
not (x1 x3 x4).
Assume H9: x1 x4 x3.
Apply H8.
Apply H0 with
x4,
x3 leaving 3 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying H6.
The subproof is completed by applying H9.
Apply unknownprop_579468dfd7f6b4a504214d51c9696047636d215697e5126a8744307125d662e6 with
x0,
x1,
x2 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Assume H7: x3 ∈ x0.
Let x4 of type ι be given.
Assume H8: x4 ∈ x0.
Let x5 of type ι be given.
Assume H9: x5 ∈ x0.
Apply H10 with
x2.
Assume H11: x3 = x4 ⟶ ∀ x6 : ο . x6.
Assume H12: x3 = x5 ⟶ ∀ x6 : ο . x6.
Assume H13: x4 = x5 ⟶ ∀ x6 : ο . x6.
Assume H14:
not (x1 x3 x4).
Assume H15:
not (x1 x3 x5).
Assume H16:
not (x1 x4 x5).
Apply FalseE with
x2.
Apply unknownprop_d5004f0fc4d2db49a1849b21a4799242aaff5503420416ca2062a6929913adc2 with
x0,
λ x6 x7 . not (x1 x6 x7),
x3,
x4,
x5 leaving 11 subgoals.
The subproof is completed by applying L6.
The subproof is completed by applying H3.
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 H11.
The subproof is completed by applying H12.
The subproof is completed by applying H13.
The subproof is completed by applying H14.
The subproof is completed by applying H15.
The subproof is completed by applying H16.
The subproof is completed by applying H4.
The subproof is completed by applying H5.