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