reserve a,b,c,d,e,f for Real,
        g           for positive Real,
        x,y         for Complex,
        S,T         for Element of REAL 2,
        u,v,w       for Element of TOP-REAL 3;
reserve a,b,c for Element of F_Real,
          M,N for Matrix of 3,F_Real;
reserve D        for non empty set;
reserve d1,d2,d3 for Element of D;
reserve A        for Matrix of 1,3,D;
reserve B        for Matrix of 3,1,D;
reserve u,v for non zero Element of TOP-REAL 3;
reserve P,Q,R for POINT of IncProjSp_of real_projective_plane,
            L for LINE of IncProjSp_of real_projective_plane,
        p,q,r for Point of real_projective_plane;

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;
