reserve x1, x2, x3, x4, x5, x6, x7 for set;

theorem Th25:
  for a, b being Real st a < b ex p1, p2 being Rational
 st a < p1 & p1 < p2 & p2 < b
proof
  let a, b be Real;
  assume a < b;
  then consider p1 being Rational such that
A1: a < p1 and
A2: p1 < b by RAT_1:7;
  ex p2 being Rational st p1 < p2 & p2 < b by A2,RAT_1:7;
  hence thesis by A1;
end;
