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

theorem
  for a, b being Real holds [. a,+infty .[ \/ {b} <> REAL
proof
  let a, b be Real;
  set ab = min (a,b) - 1;
A1: ab < min (a,b) by XREAL_1:146;
  min (a,b) <= b by XXREAL_0:17;
  then
A2: not ab in {b} by A1,TARSKI:def 1;
  min (a,b) <= a by XXREAL_0:17;
  then ab < a by XREAL_1:146,XXREAL_0:2;
  then
A3: not ab in [. a,+infty .[ by XXREAL_1:236;
  ab in REAL by XREAL_0:def 1;
  hence thesis by A3,A2,XBOOLE_0:def 3;
end;
