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 Th21:
  max(min(f,g),1_minus max(f,g)) c= 1_minus (f \+\ g)
proof
  f \+\ g c= max(f,g)\min(f,g) by Th20;
  then 1_minus (max(f,g)\min(f,g)) c= 1_minus (f \+\ g) by FUZZY_1:36;
  then
  max(1_minus max(f,g),1_minus(1_minus min(f,g))) c= 1_minus (f \+\ g) by
FUZZY_1:11;
  hence thesis;
end;
