theorem :: BKMODEL4:41

for N being invertible Matrix of 3,F_Real
for h being Element of SubGroupK-isometry
for n11, n12, n13, n21, n22, n23, n31, n32, n33 being Element of F_Real
for P being Element of BK_model st h = homography N & N = <*<*n11,n12,n13*>,<*n21,n22,n23*>,<*n31,n32,n33*>*> holds
(homography N) . P = Dir |[((((n11 * ((BK_to_REAL2 P) `1)) + (n12 * ((BK_to_REAL2 P) `2))) + n13) / (((n31 * ((BK_to_REAL2 P) `1)) + (n32 * ((BK_to_REAL2 P) `2))) + n33)),((((n21 * ((BK_to_REAL2 P) `1)) + (n22 * ((BK_to_REAL2 P) `2))) + n23) / (((n31 * ((BK_to_REAL2 P) `1)) + (n32 * ((BK_to_REAL2 P) `2))) + n33)),1]|