Let F be given.

Apply Empty_Subq_eq to the current goal.

Let y be given.

Assume Hy: y ∈ ⋃_{x ∈ Empty}F x.

Apply famunionE_impred Empty F y Hy to the current goal.

Let x be given.

Assume Hx: x ∈ Empty.

We will prove False.

An exact proof term for the current goal is EmptyE x Hx.

∎