reserve x,y,y1,y2 for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,h,g,h1 for Membership_Func of C;

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;
