reserve G for IncProjStr;
reserve a,a1,a2,b,b1,b2,c,d,p,q,r for POINT of G;
reserve A,B,C,D,M,N,P,Q,R for LINE of G;
reserve G for IncProjectivePlane;
reserve a,q for POINT of G;
reserve A,B for LINE of G;
reserve G for IncProjSp;
reserve a,b,c,d for POINT of G;
reserve P for LINE of G;
reserve G for IncProjectivePlane;

theorem Th35:
  for a,b,c being POINT of G st a on b*c holds a=c or b=c or b on c*a
proof
  let a,b,c be POINT of G;
  assume that
A1: a on b*c and
A2: a<>c and
A3: b<>c;
  c on b*c by A3,Th16;
  then
A4: {c,a} on b*c by A1,INCSP_1:1;
  b on b*c by A3,Th16;
  hence thesis by A2,A4,Def8;
end;
