theorem Th33:
  Gen w,y implies for u,v,u1,v1 being VECTOR of V holds (u,v,u1,v1
  are_Ort_wrt w,y iff PProJ (w,y,v-u,v1-u1)=0)
proof
  assume
A1: Gen w,y;
  let u,v,u1,v1 be VECTOR of V;
  u,v,u1,v1 are_Ort_wrt w,y iff v-u,v1-u1 are_Ort_wrt w,y by ANALMETR:def 3;
  hence thesis by A1,Th32;
end;
