now :: thesis: for x being object st x in { (q + p) where q is Point of T : q in X } holds
x in the carrier of T

let x be object ; :: thesis: ( x in { (q + p) where q is Point of T : q in X } implies x in the carrier of T )
assume x in { (q + p) where q is Point of T : q in X } ; :: thesis: x in the carrier of T
then ex q being Point of T st
( x = q + p & q in X ) ;
hence x in the carrier of T ; :: thesis: verum

end;

hence { (q + p) where q is Element of T : q in X } is Subset of T by TARSKI:def 3; :: thesis: verum