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
  min(f,g) c= f\(f\g)
proof
  f\(f\g) = min(f,max(1_minus f,1_minus(1_minus g))) by FUZZY_1:11
    .= max(min(f,1_minus f),min(f,g)) by FUZZY_1:9;
  hence thesis by FUZZY_1:17;
end;
