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

theorem
  for a being Real holds [. a,+infty .[ <> REAL
proof
  let a be Real;
A1: a - 1 < a by XREAL_1:146;
  a - 1 in REAL by XREAL_0:def 1;
  hence thesis by A1,XXREAL_1:236;
end;
