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;
