
theorem
  DYADIC c= [. 0,1 .]
proof
  let x be object;
  assume
A1: x in DYADIC;
  then reconsider x as Real;
A2: ex n being Nat st x in dyadic(n) by A1,URYSOHN1:def 2;
  reconsider x as R_eal by XXREAL_0:def 1;
  0 <= x & x <= 1 by A2,URYSOHN1:1;
  hence thesis by XXREAL_1:1;
end;
