theorem
  for L1,L2 being LINE of real_projective_plane holds L1 meets L2
  proof
    let L1,L2 be LINE of real_projective_plane;
    reconsider LI1 = L1,LI2 = L2 as LINE of IncProjSp_of real_projective_plane
      by INCPROJ:4;
    consider R being POINT of IncProjSp_of real_projective_plane such that
A1: R on LI1 and
A2: R on LI2 by Th62,INCPROJ:def 9;
    reconsider S = R as Element of real_projective_plane by INCPROJ:3;
    S in LI1 & S in LI2 by A1,A2,INCPROJ:5;
    hence thesis by XBOOLE_0:def 4;
  end;
