theorem Th14:
  f c= UMF(C)
proof
  let x be Element of C;
A1: 0 in REAL by XREAL_0:def 1;
A2: rng f c= [.0,1.] by RELAT_1:def 19;
  dom f = C & (UMF(C)).x = 1 by FUNCT_2:def 1,FUNCT_3:def 3;
  hence thesis by A2,Th12,A1;
end;
