reserve n for Nat;
reserve K for Field;
reserve a,b,c,d,e,f,g,h,i,a1,b1,c1,d1,e1,f1,g1,h1,i1 for Element of K;
reserve M,N for Matrix of 3,K;
reserve p for FinSequence of REAL;
reserve a,b,c,d,e,f for Real;
reserve u,u1,u2 for non zero Element of TOP-REAL 3;
reserve P for Element of ProjectiveSpace TOP-REAL 3;
reserve a,b,c,d,e,f,g,h,i for Element of F_Real;
reserve M for Matrix of 3,F_Real;
reserve e1,e2,e3,f1,f2,f3 for Element of F_Real;
reserve MABC,MAEF,MDBF,MDEC,MDEF,MDBC,MAEC,MABF,
        MABE,MACF,MBDF,MCDE,MACE,MBDE,MCDF for Matrix of 3,F_Real;
reserve r1,r2 for Real;
reserve p1,p2,p3,p4,p5,p6 for Point of TOP-REAL 3;
reserve p7,p8,p9 for Point of TOP-REAL 3;
reserve P1,P2,P3,P4,P5,P6,P7,P8,P9 for Point of ProjectiveSpace TOP-REAL 3,
                       a,b,c,d,e,f for Real;

theorem 
  not (a = 0 & b = 0 & c = 0 & d = 0 & e = 0 & f = 0) &
  {P1,P2,P3,P4,P5,P6} c= conic(a,b,c,d,e,f) &
  P1,P2,P3,P4,P5,P6,P7,P8,P9 are_in_Pascal_configuration
  implies
  P7,P8,P9 are_collinear
  proof
    per cases;
    suppose P1,P2,P3 are_collinear;
      hence thesis by Th35;
    end;
    suppose not P1,P2,P3 are_collinear;
      hence thesis by Th34;
    end;
  end;
