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 consider q being Point of (TOP-REAL n) such that
A1: ( x = t * q & q in A ) ;
thus x in the carrier of (TOP-REAL n) by A1; :: 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