the point-map of F .: K c= the Points of S2

proof

let b be set ; :: according to TARSKI:def 3 :: thesis: ( not b in the point-map of F .: K or b in the Points of S2 )
assume b in the point-map of F .: K ; :: thesis: b in the Points of S2
then ex a being set st
( a in dom the point-map of F & a in K & b = the point-map of F . a ) by FUNCT_1:def 12;
hence b in the Points of S2 by FUNCT_2:7; :: thesis: verum

end;

hence the point-map of F .: K is Subset of the Points of S2 ; :: thesis: verum