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 ι be given.
Assume H1: x2 ∈ x0.
Let x3 of type ι be given.
Assume H2: x3 ∈ x0.
Let x4 of type ι be given.
Assume H3: x4 ∈ x0.
Let x5 of type ι be given.
Assume H4: x5 ∈ x0.
Let x6 of type ι be given.
Assume H5: x6 ∈ x0.
Let x7 of type ι be given.
Assume H6: x7 ∈ x0.
Let x8 of type ι be given.
Assume H7: x8 ∈ x0.
Let x9 of type ι be given.
Assume H8: x9 ∈ x0.
Let x10 of type ι be given.
Assume H9: x10 ∈ x0.
Assume H10:
4b18d.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10.
Let x11 of type ο be given.
Assume H11:
83424.. x1 x3 x2 x4 x5 x6 x8 x7 x9 ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x1 x3 x10 ⟶ x1 x2 x10 ⟶ x1 x4 x10 ⟶ not (x1 x5 x10) ⟶ not (x1 x6 x10) ⟶ not (x1 x8 x10) ⟶ not (x1 x7 x10) ⟶ x1 x9 x10 ⟶ x11.
Apply H10 with
x11.
Assume H12:
83424.. x1 x2 x3 x4 x5 x6 x7 x8 x9.
Assume H13: x2 = x10 ⟶ ∀ x12 : ο . x12.
Assume H14: x3 = x10 ⟶ ∀ x12 : ο . x12.
Assume H15: x4 = x10 ⟶ ∀ x12 : ο . x12.
Assume H16: x5 = x10 ⟶ ∀ x12 : ο . x12.
Assume H17: x6 = x10 ⟶ ∀ x12 : ο . x12.
Assume H18: x7 = x10 ⟶ ∀ x12 : ο . x12.
Assume H19: x8 = x10 ⟶ ∀ x12 : ο . x12.
Assume H20: x9 = x10 ⟶ ∀ x12 : ο . x12.
Assume H21: x1 x2 x10.
Assume H22: x1 x3 x10.
Assume H23: x1 x4 x10.
Assume H24:
not (x1 x5 x10).
Assume H25:
not (x1 x6 x10).
Assume H26:
not (x1 x7 x10).
Assume H27:
not (x1 x8 x10).
Assume H28: x1 x9 x10.
Apply H11 leaving 17 subgoals.
Apply unknownprop_e9e4030b2a2f57a56e46c393da5267108e68f3cac79a8a24c8214037e1971148 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
x9 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 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 H12.
The subproof is completed by applying H14.
The subproof is completed by applying H13.
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 H19.
The subproof is completed by applying H18.
The subproof is completed by applying H20.
The subproof is completed by applying H22.
The subproof is completed by applying H21.
The subproof is completed by applying H23.
The subproof is completed by applying H24.
The subproof is completed by applying H25.
The subproof is completed by applying H27.
The subproof is completed by applying H26.
The subproof is completed by applying H28.