I would like to use the infinite join (supremum) operator as a subscript in a math paper. However, for example $\mathscr{F}_{\bigvee_{i\in I}x_i}$ produces the normal size operator in the subscript (see attached picture, on the left), while $\mathscr{F}_{\vee_{i\in I}x_i}$ looks pretty ugly to my taste (see the picture, on the right).
Could you please help me to put the operator in the subscript in proper size and esthetic shape? I wasn't able to find a solution but I have seen elegant subscript supremum operators used in mathematical texts.
EDIT: Below is the example of what I have in mind:







$\mathscr{F}_{{\displaystyle\vee}_{i\in I}x_i}$– Steven B. Segletes Dec 29 '16 at 18:37