reserve A,A1,A2,B,B1,B2,C,O for Ordinal,
      R,S for Relation,
      a,b,c,o,l,r for object;

theorem Th16:
  OpenProd(R,A,B) c= ClosedProd(R,A,B)
proof
  let x,y be object;
  assume A1:[x,y] in OpenProd(R,A,B);
  then A2: x in Day(R,A) & y in Day(R,A) by ZFMISC_1:87;
  then (born(R,x) in A & born(R,y) in A) or
  (born(R,x) = A & born(R,y) in B) or
  (born(R,x) in B & born(R,y) = A) by A1,Def9;
  then (born(R,x) in A & born(R,y) in A) or
  (born(R,x) = A & born(R,y) c= B) or
  (born(R,x) c= B & born(R,y) = A) by ORDINAL1:def 2;
  hence thesis by A2,Def10;
end;
