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;

theorem Th78:
  g in product f implies g|A in sproduct f
proof
A1: product f c= sproduct f by Th51;
  assume g in product f;
  hence thesis by A1,Th64,RELAT_1:59;
end;
