
theorem
  for l1,n2,m,n1,m1,l,n being Element of ProjectiveLines
  real_projective_plane holds
  (l1,n2,m are_concurrent & n1,m1,m are_concurrent & l1,n1,l are_concurrent &
  n2,m1,l are_concurrent & l1,m1,n are_concurrent & n2,n1,n are_concurrent &
  l,m,n are_concurrent implies
  (l1,n2,m1 are_concurrent or l1,n2,n1 are_concurrent or
  l1,n1,m1 are_concurrent or n2,n1,m1 are_concurrent))
  proof
    let l1,n2,m,n1,m1,l,n be Element of ProjectiveLines real_projective_plane;
    assume that
A1: l1,n2,m are_concurrent and
A2: n1,m1,m are_concurrent and
A3: l1,n1,l are_concurrent and
A4: n2,m1,l are_concurrent and
A5: l1,m1,n are_concurrent and
A6: n2,n1,n are_concurrent and
A7: l,m,n are_concurrent;
    dual l1,dual n2,dual m are_collinear &
      dual n1,dual m1,dual m are_collinear &
      dual l1,dual n1,dual l are_collinear &
      dual n2,dual m1,dual l are_collinear &
      dual l1,dual m1,dual n are_collinear &
      dual n2,dual n1,dual n are_collinear &
      dual l,dual m,dual n are_collinear by A1,A2,A3,A4,A5,A6,A7,Th60;
    then dual l1,dual n2,dual m1 are_collinear or
      dual l1,dual n2,dual n1 are_collinear or
      dual l1,dual n1,dual m1 are_collinear or
      dual n2,dual n1,dual m1 are_collinear by ANPROJ_2:def 11;
    hence thesis by Th60;
  end;
