reserve P for Element of BK_model;
reserve N,N1,N2 for invertible Matrix of 3,F_Real;
reserve l,l1,l2 for Element of the Lines of IncProjSp_of real_projective_plane;
reserve P for Point of ProjectiveSpace TOP-REAL 3,
        l for LINE of IncProjSp_of real_projective_plane;

theorem Th22:
  for a being non zero Real
  for b,c being Real holds a * |[b / a,c / a,1]| = |[b,c,a]|
  proof
    let a be non zero Real;
    let b,c be Real;
    a * |[b / a,c / a,1]| = |[a * (b / a), a * (c / a),a * 1]| by EUCLID_5:8
                         .= |[b , a * (c / a),a]| by XCMPLX_1:87
                         .= |[b, c ,a]| by XCMPLX_1:87;
    hence thesis;
  end;
