Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Let x2 of type ι be given.
Assume H0: x2 ∈ x0.
Apply prop_ext_2 with
decode_p (Sep x0 x1) x2,
x1 x2 leaving 2 subgoals.
Assume H1:
x2 ∈ Sep x0 x1.
Apply SepE2 with
x0,
x1,
x2.
The subproof is completed by applying H1.
Assume H1: x1 x2.
Apply SepI with
x0,
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.