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

theorem
  for a being Real holds ]. -infty, a .] <> REAL
proof
  let a be Real;
A1: a + 1 > a by XREAL_1:29;
  a + 1 in REAL by XREAL_0:def 1;
  hence thesis by A1,XXREAL_1:234;
end;
