Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 x3 . x1 x2 x3 ⟶ x1 x3 x2.
Assume H1:
∀ x2 . x2 ⊆ x0 ⟶ atleastp u3 x2 ⟶ not (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ x1 x3 x4).
Assume H2:
∀ x2 . x2 ⊆ x0 ⟶ atleastp u6 x2 ⟶ not (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ not (x1 x3 x4)).
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Assume H4: x2 ⊆ x0.
Assume H5: x3 ⊆ x0.
Assume H6: x4 ⊆ x0.
Assume H7: x5 ⊆ x0.
Assume H8:
∀ x6 . x6 ∈ x4 ⟶ nIn x6 x2.
Assume H9:
∀ x6 . x6 ∈ x4 ⟶ nIn x6 x3.
Assume H10:
∀ x6 . x6 ∈ x4 ⟶ nIn x6 x5.
Assume H11:
∀ x6 . x6 ∈ x2 ⟶ nIn x6 x3.
Assume H12:
∀ x6 . x6 ∈ x2 ⟶ nIn x6 x5.
Assume H13:
∀ x6 . x6 ∈ x3 ⟶ nIn x6 x5.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Let x10 of type ι be given.
Let x11 of type ι be given.
Let x12 of type ι be given.
Let x13 of type ι be given.
Let x14 of type ι be given.
Let x15 of type ι be given.
Assume H14: x6 ∈ x4.
Assume H15: x7 ∈ x4.
Assume H17: x14 ∈ x2.
Assume H18: x15 ∈ x5.
Assume H19: x7 = x6 ⟶ ∀ x16 : ο . x16.
Assume H20: x8 = x6 ⟶ ∀ x16 : ο . x16.
Assume H21: x9 = x6 ⟶ ∀ x16 : ο . x16.
Assume H22: x8 = x7 ⟶ ∀ x16 : ο . x16.
Assume H23: x9 = x7 ⟶ ∀ x16 : ο . x16.
Assume H24: x9 = x8 ⟶ ∀ x16 : ο . x16.
Assume H25: x1 x6 x7.
Assume H26: x1 x7 x8.
Assume H27: x1 x8 x9.
Assume H28: x1 x9 x6.
Assume H29: x1 x6 x10.
Assume H30: x1 x6 x15.
Assume H31: x1 x7 x14.
Assume H32: x1 x7 x11.
Assume H33: x1 x12 x15.
Assume H34:
not (x1 x14 x6).
Apply unknownprop_f5f104e32284035daf22b65668a507b9fdee3549a3de7b7bfd58db4049fc9d40 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
x9,
x10,
x11,
x12,
x13,
x14,
x15 leaving 26 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.
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 H17.
The subproof is completed by applying H18.
The subproof is completed by applying L35.
The subproof is completed by applying H25.
The subproof is completed by applying H29.
The subproof is completed by applying H30.
The subproof is completed by applying H31.
The subproof is completed by applying H32.