{ [.a,b.] where a, b is Real : verum } c= bool REAL

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in { [.a,b.] where a, b is Real : verum } or x in bool REAL )
assume x in { [.a,b.] where a, b is Real : verum } ; :: thesis: x in bool REAL
then ex a0, b0 being Real st x = [.a0,b0.] ;
hence x in bool REAL ; :: thesis: verum

end;

hence { [.a,b.] where a, b is Real : verum } is Subset-Family of REAL ; :: thesis: verum