now

let x be set ; :: thesis: ( x in { (t * a) where a is Point of (TOP-REAL n) : a in A } implies x in the carrier of (TOP-REAL n) )
assume x in { (t * a) where a is Point of (TOP-REAL n) : a in A } ; :: thesis: x in the carrier of (TOP-REAL n)
then ex q being Point of (TOP-REAL n) st
( x = t * q & q in A ) ;
hence x in the carrier of (TOP-REAL n) ; :: thesis: verum

end;

hence { (t * a) where a is Point of (TOP-REAL n) : a in A } is Subset of (TOP-REAL n) by TARSKI:def 3; :: thesis: verum