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.
Apply unknownprop_59b1aa4b45a22b67f6c8a9fb07eee01282476217228ecde8a9b0a7811abc9d77 with
x0,
x1,
x2,
x3,
x5,
x4 leaving 6 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 H4.
The subproof is completed by applying H3.
Apply unknownprop_655fa89ff16d02cb5c6a126e8512fcf2710b55de67013efaccd39a53061ed8f8 with
x0,
x1,
x5,
x4,
x2,
x3 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_59b1aa4b45a22b67f6c8a9fb07eee01282476217228ecde8a9b0a7811abc9d77 with
x0,
x1,
x4,
x5,
x2,
x3 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_655fa89ff16d02cb5c6a126e8512fcf2710b55de67013efaccd39a53061ed8f8 with
x0,
x1,
x2,
x3,
x4,
x5 leaving 6 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.