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
  not p on K & not p on L & y in rng IncProj(K,p,L) implies y on L
proof
  assume that
A1: ( not p on K)& not p on L and
A2: y in rng IncProj(K,p,L);
  consider x being POINT of IPP such that
A3: x in dom IncProj(K,p,L) and
A4: y = IncProj(K,p,L).x by A2,PARTFUN1:3;
  x on K by A1,A3,Def1;
  hence thesis by A1,A4,Th20;
end;
