Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Let x2 of type ι be given.
Assume H0:
nIn x2 (Sep x0 (λ x3 . x1 x3)).
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x2,
Sep x0 (λ x3 . x1 x3) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_646b3add51cf8f8e84959b456822a93c7e59b2f394a14897b6752b9d28c1a75d with
x0,
x1,
x2 leaving 2 subgoals.
Apply unknownprop_75b5762e65badae8f9531d40fddd332ff95b59f608d93c7a55f19f4fa5ef37d5 with
x2,
x0.
The subproof is completed by applying H1.
Apply unknownprop_b777a79c17f16cd28153af063df26a4626b11c1f1d4394d7f537c11837ab0962 with
x1 x2.
The subproof is completed by applying H2.