reserve IPP for IncProjSp;
reserve a,b,c,d,p,q,o,r,s,t,u,v,w,x,y for POINT of IPP;
reserve A,B,C,D,L,P,Q,S for LINE of IPP;

theorem Th1:
  ex a st not a on A
proof
  consider p,L such that
A1: not p on L by INCPROJ:def 6;
  now
    assume
A2: A<>L;
    now
      consider q,r,s such that
A3:   q<>r and
      r<>s and
      s<>q and
A4:   q on L & r on L and
      s on L by INCPROJ:def 7;
      not q on A or not r on A by A2,A3,A4,INCPROJ:def 4;
      hence thesis;
    end;
    hence thesis;
  end;
  hence thesis by A1;
end;
