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 Th20:
  not p on K & not p on L & x on K & y = IncProj (K,p,L).x implies y on L
proof
  assume
A1: ( not p on K)& not p on L & x on K & y = IncProj(K,p,L).x;
  consider X such that
A2: p on X & x on X by INCPROJ:def 5;
  ex z being POINT of IPP st z on L & z on X by INCPROJ:def 9;
  hence thesis by A1,A2,Def1;
end;
