theorem Th25:
  Gen w,y implies for p,q,r holds p,q _|_ r,r
proof
  assume
A1: Gen w,y;
  let p,q,r;
  reconsider u=p,v=q,u1=r as Element of V;
  u1-u1 = 0.V by RLVECT_1:15;
  then v-u,u1-u1 are_Ort_wrt w,y by A1,Th5;
  then u,v,u1,u1 are_Ort_wrt w,y;
  hence thesis by Th21;
end;
