Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Let x2 of type ι → ι be given.
Let x3 of type ι be given.
Assume H0: x3 ∈ {x2 x4|x4 ∈ x0,x1 x4}.
Let x4 of type ο be given.
Assume H1: ∀ x5 . x5 ∈ x0 ⟶ x1 x5 ⟶ x3 = x2 x5 ⟶ x4.
Apply ReplSepE with
x0,
x1,
x2,
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x5 of type ι be given.
Assume H2:
(λ x6 . and (and (x6 ∈ x0) (x1 x6)) (x3 = x2 x6)) x5.
Apply H2 with
x4.
Assume H3:
and (x5 ∈ x0) (x1 x5).
Apply H3 with
x3 = x2 x5 ⟶ x4.
The subproof is completed by applying H1 with x5.