reserve V for RealLinearSpace;
reserve u,u1,u2,v,v1,v2,w,w1,y for VECTOR of V;
reserve a,a1,a2,b,b1,b2,c1,c2 for Real;
reserve x,z for set;

theorem
  w,y are_Ort_wrt w,y
proof
A1: y = 0.V + y by RLVECT_1:4
    .= 0.V + 1*y by RLVECT_1:def 8
    .= 0*w + 1*y by RLVECT_1:10;
A2: 1*0 + 0*1 = 0;
  w = w + 0.V by RLVECT_1:4
    .= 1*w + 0.V by RLVECT_1:def 8
    .= 1*w + 0*y by RLVECT_1:10;
  hence thesis by A1,A2;
end;
