theorem Th23:
  p,q _|_ p1,q1 implies p1,q1 _|_ p,q
proof
  reconsider u=p,v=q,u1=p1,v1=q1 as Element of V;
  assume p,q _|_ p1,q1;
  then u,v,u1,v1 are_Ort_wrt w,y by Th21;
  then v-u,v1-u1 are_Ort_wrt w,y;
  then v1-u1,v-u are_Ort_wrt w,y;
  then u1,v1,u,v are_Ort_wrt w,y;
  hence thesis by Th21;
end;
