reserve n   for Nat,
        r,s for Real,
        x,y for Element of REAL n,
        p,q for Point of TOP-REAL n,
        e   for Point of Euclid n;
reserve n for non zero Nat;
reserve n for non zero Nat;
reserve n for Nat,
        X for set,
        S for Subset-Family of X;
reserve n for Nat,
        S for Subset-Family of REAL;
reserve n       for Nat,
        a,b,c,d for Element of REAL n;

theorem
  a <= b implies ClosedHyperInterval(a,b) is non empty
  proof
    assume a <= b; then
    ClosedHyperInterval(a,a) c= ClosedHyperInterval(a,b) by Th49;
    then {a} c= ClosedHyperInterval(a,b) by Th48;
    hence thesis;
  end;
