theorem :: BKMODEL2:61

for P, Q, R, S, T, U being Element of BK_model st ex h1, h2 being Element of SubGroupK-isometry ex N1, N2 being invertible Matrix of 3,F_Real st
( h1 = homography N1 & h2 = homography N2 & (homography N1) . P = R & (homography N1) . Q = S & (homography N2) . R = T & (homography N2) . S = U ) holds
ex h3 being Element of SubGroupK-isometry ex N3 being invertible Matrix of 3,F_Real st
( h3 = homography N3 & (homography N3) . P = T & (homography N3) . Q = U )