theorem Th30:
  Gen w,y & p,q _|_ p,q implies p = q
proof
  assume that
A1: Gen w,y and
A2: p,q _|_ p,q;
  reconsider u=p,v=q as Element of V;
  u,v,u,v are_Ort_wrt w,y by A2,Th21;
  then v-u,v-u are_Ort_wrt w,y;
  then v-u = 0.V by A1,Th11;
  hence thesis by RLVECT_1:21;
end;
