set X = { (g * h) where g, h is Element of G : ( g in A & h in B ) } ;
{ (g * h) where g, h is Element of G : ( g in A & h in B ) } c= the carrier of G

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in { (g * h) where g, h is Element of G : ( g in A & h in B ) } or x in the carrier of G )
assume x in { (g * h) where g, h is Element of G : ( g in A & h in B ) } ; :: thesis: x in the carrier of G
then ex g, h being Element of G st
( x = g * h & g in A & h in B ) ;
hence x in the carrier of G ; :: thesis: verum

end;

hence { (g * h) where g, h is Element of G : ( g in A & h in B ) } is Subset of G ; :: thesis: verum