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:
58366.. x1 x2 x3 x4 x5 x6 x7 x8.
Apply unknownprop_8bfde236d320d47824686c4918d7f78248b15954915942121a0fb254f3586bbb with
x0,
x1,
x2,
x3,
x4,
x6,
x5,
x7,
x8 leaving 9 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 H5.
The subproof is completed by applying H4.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
Apply unknownprop_a5933b738b6a6509fb7e33ebfa90c8459842c638c3af489cfebf3e8a3c521b9c with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8 leaving 9 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.