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;
reserve IPP for Fanoian IncProjSp;
reserve a,b,c,d,p,q,r,s for POINT of IPP;
reserve A,B,C,D,L,Q,R,S for LINE of IPP;
reserve IPP for Desarguesian 2-dimensional IncProjSp;
reserve c,p,q,x,y for POINT of IPP;
reserve A,B,C,D,K,L,R,X for LINE of IPP;
reserve f for PartFunc of the Points of IPP,the Points of IPP;

theorem Th19:
  not p on K & not p on L & x on K implies IncProj(K,p,L).x is POINT of IPP
proof
  assume ( not p on K)& not p on L & x on K;
  then x in dom IncProj(K,p,L) by Def1;
  hence thesis by PARTFUN1:4;
end;
