for a, b, c, d, e, f being Real
for P1, P2, P3, P4, P5, P6 being Point of (ProjectiveSpace (TOP-REAL 3))
for N being invertible Matrix of 3,F_Real st ( not a = 0 or not b = 0 or not c = 0 or not d = 0 or not e = 0 or not f = 0 ) & P1 in conic (a,b,c,d,e,f) & P2 in conic (a,b,c,d,e,f) & P3 in conic (a,b,c,d,e,f) & P4 in conic (a,b,c,d,e,f) & P5 in conic (a,b,c,d,e,f) & P6 in conic (a,b,c,d,e,f) holds
ex a2, b2, c2, d2, e2, f2 being Real st
( ( not a2 = 0 or not b2 = 0 or not c2 = 0 or not d2 = 0 or not e2 = 0 or not f2 = 0 ) & (homography N) . P1 in conic (a2,b2,c2,d2,e2,f2) & (homography N) . P2 in conic (a2,b2,c2,d2,e2,f2) & (homography N) . P3 in conic (a2,b2,c2,d2,e2,f2) & (homography N) . P4 in conic (a2,b2,c2,d2,e2,f2) & (homography N) . P5 in conic (a2,b2,c2,d2,e2,f2) & (homography N) . P6 in conic (a2,b2,c2,d2,e2,f2) )