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
  for a,b,c,d being POINT of G st a*c = b*d holds a = c or b = d or c =
  d or a on c*d
proof
  let a,b,c,d be POINT of G;
  assume that
A1: a*c = b*d and
A2: not a = c and
A3: ( not b = d)& not c = d;
  a*c = c*d by A1,A2,A3,Th28;
  hence thesis by A2,Th16;
end;
