
theorem RealNon:
  for a,b being Real st a <= b holds
    REAL \ ].a,b.[ <> {}
  proof
    let a,b be Real;
    assume a <= b;
    consider c being Real such that
A1: c < a by XREAL_1:2;
A2: not c in ].a,b.[ by A1,XXREAL_1:4;
    c in REAL by XREAL_0:def 1;
    hence thesis by A2,XBOOLE_0:def 5;
  end;
