reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;
reserve A,B for Ordinal;
reserve n,k for Nat;

theorem Th98:
  for S being functional set, f be Function, i be set
     st f in S & i in dom product" S holds f.i in (product" S).i
proof
  let S being functional set, F be Function, i be set such that
A1: F in S;
  assume i in dom product" S;
   then (product" S).i = the set of all f.i where f is Element of S
      by A1,Th73;
 hence F.i in (product" S).i by A1;
end;
