reserve IPS for IncProjSp,
  z for POINT of IPS;
reserve IPP for Desarguesian 2-dimensional IncProjSp,
  a,b,c,d,p,pp9,q,o,o9,o99 ,oo9 for POINT of IPP,
  r,s,x,y,o1,o2 for POINT of IPP,
  O1,O2,O3,O4,A,B,C,O,Q,Q1 ,Q2,Q3,R,S,X for LINE of IPP;

theorem
  for f being Projection of IPP holds f" is Projection of IPP
proof
  let f be Projection of IPP;
  consider a,A,B such that
A1: ( not a on A)& not a on B and
A2: f = IncProj(A,a,B) by Def3;
  f" = IncProj (B,a,A) by A1,A2,Th8;
  hence thesis by A1,Def3;
end;
