reserve G for IncProjStr;
reserve a,a1,a2,b,b1,b2,c,d,p,q,r for POINT of G;
reserve A,B,C,D,M,N,P,Q,R for LINE of G;

theorem
  G is configuration iff for p,q,P,Q st p on P,Q & q on P,Q holds p
  = q or P = Q
proof
  thus G is configuration implies for p,q,P,Q st p on P,Q & q on P,Q holds
  p = q or P = Q;
  hereby
    assume
A1: for p,q,P,Q st p on P,Q & q on P,Q holds p = q or P = Q;
    now
      let p,q,P,Q;
      assume p on P & q on P & p on Q & q on Q;
      then p on P,Q & q on P,Q;
      hence p = q or P = Q by A1;
    end;
    hence G is configuration;
  end;
end;
