theorem
  conic(0,0,0,0,0,0) = the carrier of ProjectiveSpace TOP-REAL 3
  proof
    now
      let o be object;
      assume
A1:   o in the carrier of ProjectiveSpace TOP-REAL 3;
      for u be Element of TOP-REAL 3 st u is non zero & o = Dir u
        holds qfconic(0,0,0,0,0,0,u) = 0;
      hence o in conic(0,0,0,0,0,0) by A1;
    end;
    then the carrier of ProjectiveSpace TOP-REAL 3 c= conic(0,0,0,0,0,0)
      by TARSKI:def 3;
    hence thesis by XBOOLE_0:def 10;
  end;
