reserve n,m,k,i for Nat,
  h,r,r1,r2,x0,x1,x2,x for Real,
  S for Functional_Sequence of REAL,REAL,
  y for set;
reserve f,f1,f2 for Function of REAL,REAL;

theorem
  f is constant implies [!f,x0,x1!] = 0
proof
  x0 in REAL by XREAL_0:def 1;
  then
A1: x0 in dom f by FUNCT_2:def 1;
  x1 in REAL by XREAL_0:def 1;
  then
A2: x1 in dom f by FUNCT_2:def 1;
  assume f is constant;
  then f.x0 = f.x1 by A1,A2,FUNCT_1:def 10;
  hence thesis;
end;
