defpred S_{1}[ Element of FMT] means ex V being Subset of FMT st

( V in U_FMT $1 & V c= A );

{ x where x is Element of FMT : S_{1}[x] } is Subset of FMT
from DOMAIN_1:sch 7();

hence { x where x is Element of FMT : ex V being Subset of FMT st

( V in U_FMT x & V c= A ) } is Subset of FMT ; :: thesis: verum

( V in U_FMT $1 & V c= A );

{ x where x is Element of FMT : S

hence { x where x is Element of FMT : ex V being Subset of FMT st

( V in U_FMT x & V c= A ) } is Subset of FMT ; :: thesis: verum