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 Th1:
  for x be Element of C,h be Membership_Func of C holds 0 <= h.x & h.x <= 1
proof
  let x be Element of C,h be Membership_Func of C;
  (EMF C).x = 0 by FUNCT_3:def 3;
  hence 0 <= h.x by FUZZY_1:16;
  (UMF C).x = 1 by FUNCT_3:def 3;
  hence thesis by FUZZY_1:16;
end;
