
theorem
  for l1,l2,l3 being LINE of IncProjSp_of real_projective_plane holds
  l1,l2,l3 are_concurrent iff #l1,#l2,#l3 are_concurrent
  proof
    let l1,l2,l3 be LINE of IncProjSp_of real_projective_plane;
    reconsider l91 = #l1, l92 = #l2, l93 = #l3 as
      Element of ProjectiveLines real_projective_plane;
    hereby
      assume l1,l2,l3 are_concurrent;
      then #l91,#l92,#l93 are_concurrent;
      hence #l1,#l2,#l3 are_concurrent by Th49;
    end;
    assume #l1,#l2,#l3 are_concurrent;
    then ##l1,##l2,##l3 are_concurrent by Th49;
    hence l1,l2,l3 are_concurrent;
  end;
