now

let x be set ; :: thesis: ( x in { y where y is Point of (TOP-REAL n) : B + y c= X } implies x in the carrier of (TOP-REAL n) )
assume x in { y where y is Point of (TOP-REAL n) : B + y c= X } ; :: thesis: x in the carrier of (TOP-REAL n)
then consider q being Point of (TOP-REAL n) such that
A1: ( x = q & B + q c= X ) ;
thus x in the carrier of (TOP-REAL n) by A1; :: thesis: verum

end;

hence { y where y is Point of (TOP-REAL n) : B + y c= X } is Subset of (TOP-REAL n) by TARSKI:def 3; :: thesis: verum