:: deftheorem defines is_automorphism_of TRANSGEO:def 3 :
for A being non empty set
for f being Permutation of A
for R being Relation of [:A,A:] holds
( f is_automorphism_of R iff for x, y, z, t being Element of A holds
( [[x,y],[z,t]] in R iff [[(f . x),(f . y)],[(f . z),(f . t)]] in R ) );