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 Th49:
  for c be Element of C,f,g be Membership_Func of C holds (f ++ g)
  .c = 1 - ((1 - f.c)*(1 - g.c))
proof
  let c;
  let g,h be Membership_Func of C;
  (g ++ h).c = (1_minus((1_minus g)*(1_minus h))).c by Th36
    .= 1-((1_minus g)*(1_minus h)).c by FUZZY_1:def 5
    .= 1-((1_minus g).c)*((1_minus h).c) by Def2
    .= 1-((1-g.c)*((1_minus h).c)) by FUZZY_1:def 5;
  hence thesis by FUZZY_1:def 5;
end;
