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.
Assume H7:
af3c4.. x1 x2 x3 x4 x5 x6 x7.
Let x8 of type ο be given.
Assume H8:
80df3.. x1 x2 x5 x4 x3 x6 ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x1 x2 x7 ⟶ x1 x5 x7 ⟶ x1 x4 x7 ⟶ x1 x3 x7 ⟶ not (x1 x6 x7) ⟶ x8.
Apply H7 with
x8.
Assume H9:
80df3.. x1 x2 x3 x4 x5 x6.
Assume H10: x2 = x7 ⟶ ∀ x9 : ο . x9.
Assume H11: x3 = x7 ⟶ ∀ x9 : ο . x9.
Assume H12: x4 = x7 ⟶ ∀ x9 : ο . x9.
Assume H13: x5 = x7 ⟶ ∀ x9 : ο . x9.
Assume H14: x6 = x7 ⟶ ∀ x9 : ο . x9.
Assume H15: x1 x2 x7.
Assume H16: x1 x3 x7.
Assume H17: x1 x4 x7.
Assume H18: x1 x5 x7.
Assume H19:
not (x1 x6 x7).
Apply H8 leaving 11 subgoals.
Apply unknownprop_bf131b5b8f3c5e2350de21c2a38259a206a2a2d0c8058ae870906798db398ce9 with
x0,
x1,
x2,
x3,
x4,
x5,
x6 leaving 7 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 H9.
The subproof is completed by applying H10.
The subproof is completed by applying H13.
The subproof is completed by applying H12.
The subproof is completed by applying H11.
The subproof is completed by applying H14.
The subproof is completed by applying H15.
The subproof is completed by applying H18.
The subproof is completed by applying H17.
The subproof is completed by applying H16.
The subproof is completed by applying H19.