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.
Assume H8:
88b7c.. x1 x2 x3 x4 x5 x6 x7 x8.
Let x9 of type ο be given.
Assume H9:
f6f09.. x1 x2 x4 x3 x6 x5 x7 ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ x1 x2 x8 ⟶ x1 x4 x8 ⟶ x1 x3 x8 ⟶ not (x1 x6 x8) ⟶ not (x1 x5 x8) ⟶ not (x1 x7 x8) ⟶ x9.
Apply H8 with
x9.
Assume H10:
f6f09.. x1 x2 x3 x4 x5 x6 x7.
Assume H11: x2 = x8 ⟶ ∀ x10 : ο . x10.
Assume H12: x3 = x8 ⟶ ∀ x10 : ο . x10.
Assume H13: x4 = x8 ⟶ ∀ x10 : ο . x10.
Assume H14: x5 = x8 ⟶ ∀ x10 : ο . x10.
Assume H15: x6 = x8 ⟶ ∀ x10 : ο . x10.
Assume H16: x7 = x8 ⟶ ∀ x10 : ο . x10.
Assume H17: x1 x2 x8.
Assume H18: x1 x3 x8.
Assume H19: x1 x4 x8.
Assume H20:
not (x1 x5 x8).
Assume H21:
not (x1 x6 x8).
Assume H22:
not (x1 x7 x8).
Apply H9 leaving 13 subgoals.
Apply unknownprop_7dca439035292d2c65491213a1796123a71a23fd6fee4ed8cfb3fb60c8dd8aa9 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7 leaving 8 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 H10.
The subproof is completed by applying H11.
The subproof is completed by applying H13.
The subproof is completed by applying H12.
The subproof is completed by applying H15.
The subproof is completed by applying H14.
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 H21.
The subproof is completed by applying H20.
The subproof is completed by applying H22.