reserve a,b,c,d,e,f,g,h,i for Real,
                        M for Matrix of 3,REAL;
reserve                           PCPP for CollProjectiveSpace,
        c1,c2,c3,c4,c5,c6,c7,c8,c9,c10 for Element of PCPP;
reserve o,p1,p2,p3,q1,q2,q3,r1,r2,r3 for Element of ProjectiveSpace TOP-REAL 3;
reserve v0,v1,v2,v3,v4,
        c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,
        v100,v101,v102,v103 for Element of ProjectiveSpace TOP-REAL 3;

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;
