theorem Th55: :: AFF_4:55

for AS being AffinSpace
for X, Y being Subset of AS st X is being_plane & Y is being_plane holds
( X '||' Y iff ex A, P, M, N being Subset of AS st
( not A // P & A c= X & P c= X & M c= Y & N c= Y & ( A // M or M // A ) & ( P // N or N // P ) ) )