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:
5e84d.. x1 x2 x3 x4 x5 x6 x7.
Apply unknownprop_c05dc5c509e1f92b8234d6e23675c80dd86d32981be20a6277b34f12801d25f7 with
x0,
x1,
x2,
x3,
x7,
x5,
x6,
x4 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 H6.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H3.
Apply unknownprop_9846198a10bdb5a8c939f2ae6fd28a3970c853a734542f380fb05e775147acd3 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 H7.