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 Th2:
  G is configuration iff for p,q,P,Q st {p,q} on P & {p,q} on Q
  holds p = q or P = Q
proof
  hereby
    assume
A1: G is configuration;
    let p,q,P,Q;
    assume that
A2: {p,q} on P and
A3: {p,q} on Q;
A4: p on Q & q on Q by A3,INCSP_1:1;
    p on P & q on P by A2,INCSP_1:1;
    hence p = q or P = Q by A1,A4;
  end;
  hereby
    assume
A5: for p,q,P,Q st {p,q} on P & {p,q} on 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,q} on P & {p,q} on Q by INCSP_1:1;
      hence p = q or P = Q by A5;
    end;
    hence G is configuration;
  end;
end;
