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 G being IncProjSp, a,b,q,q1 being POINT of G st q on a*b & q on a*
  q1 & q<>a & q1<>a & a<>b holds q1 on a*b
proof
  let G be IncProjSp, a,b,q,q1 be POINT of G;
  assume that
A1: q on a*b & q on a*q1 & q<>a and
A2: q1<>a and
A3: a<>b;
  a on a*b & a on a*q1 by A2,A3,Th16;
  then a*b = a*q1 by A1,INCPROJ:def 4;
  hence thesis by A2,Th16;
end;
