reserve n for Nat;
reserve K for Field;
reserve a,b,c,d,e,f,g,h,i,a1,b1,c1,d1,e1,f1,g1,h1,i1 for Element of K;
reserve M,N for Matrix of 3,K;
reserve p for FinSequence of REAL;
reserve a,b,c,d,e,f for Real;
reserve u,u1,u2 for non zero Element of TOP-REAL 3;
reserve P for Element of ProjectiveSpace TOP-REAL 3;

theorem Th11:
  P = Dir u & qfconic(a,b,c,d,e,f,u) = 0 implies
  P in conic(a,b,c,d,e,f)
  proof
    assume that
A2: P = Dir u and
A3: qfconic(a,b,c,d,e,f,u) = 0;
    for v be Element of TOP-REAL 3 st v is non zero & P = Dir v holds
    qfconic(a,b,c,d,e,f,v) = 0 by A2,A3,Th10;
    hence thesis;
  end;
