reserve a,b,c,d,e,f,g,h,i for Real,
                        M for Matrix of 3,REAL;
reserve                           PCPP for CollProjectiveSpace,
        c1,c2,c3,c4,c5,c6,c7,c8,c9,c10 for Element of PCPP;

theorem Th6:
  not c1,c4,c7 are_collinear &
  c1,c4,c2 are_collinear & c1,c4,c3 are_collinear &
  c1,c7,c5 are_collinear & c1,c7,c6 are_collinear &
  c4,c5,c8 are_collinear & c7,c2,c8 are_collinear &
  c4,c6,c9 are_collinear & c3,c7,c9 are_collinear &
  c2,c6,c10 are_collinear & c3,c5,c10 are_collinear
  implies
  c4,c2,c3 are_collinear & c4,c5,c8 are_collinear &
  c4,c9,c6 are_collinear & c7,c5,c6 are_collinear &
  c7,c9,c3 are_collinear & c7,c2,c8 are_collinear &
  c10,c2,c6 are_collinear & c10,c5,c3 are_collinear
  proof
    assume that
A1: not c1,c4,c7 are_collinear and
A2: c1,c4,c2 are_collinear and
A3: c1,c4,c3 are_collinear and
A4: c1,c7,c5 are_collinear and
A5: c1,c7,c6 are_collinear and
A6: c4,c5,c8 are_collinear and
A7: c7,c2,c8 are_collinear and
A8: c4,c6,c9 are_collinear and
A9: c3,c7,c9 are_collinear and
A10: c2,c6,c10 are_collinear and
A11: c3,c5,c10 are_collinear;
    not c7=c1 & not c4=c1 & c1,c4,c4 are_collinear & c1,c7,c7 are_collinear
      by A1,COLLSP:2;
    hence thesis
      by A2,COLLSP:3,A3,A11,HESSENBE:1,A10,A9,A8,A7,A6,A4,A5;
  end;
