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;
reserve C1,C2 for non empty set;
reserve f,g for RMembership_Func of C1,C2;

theorem
  max(f,Umf(C1,C2)) = Umf(C1,C2) & min(f,Umf(C1,C2)) = f & max(f,Zmf(C1,
  C2)) = f & min(f,Zmf(C1,C2)) = Zmf(C1,C2)
proof
A1: Umf(C1,C2) = UMF [:C1,C2:];
  Zmf(C1,C2) = EMF [:C1,C2:];
  hence thesis by A1,FUZZY_1:18;
end;
