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
  max(f\ max(g,h),min(min(f,g),h)) c= f\(g \+\ h)
proof
  max(f\ max(g,h),min(min(f,g),h)) = max(min(f,1_minus max(g,h)),min(f,min
  (g,h))) by FUZZY_1:7
    .= min(f,max(1_minus max(g,h),min(g,h))) by FUZZY_1:9;
  hence thesis by Th21,FUZZY_1:25;
end;
