:: deftheorem defines is_atlas_of MIDSP_2:def 3 :
for S being non empty set
for G being non empty addLoopStr
for w being Function of [:S,S:], the carrier of G holds
( w is_atlas_of S,G iff ( ( for a being Element of S
for x being Element of G ex b being Element of S st w . (a,b) = x ) & ( for a, b, c being Element of S st w . (a,b) = w . (a,c) holds
b = c ) & ( for a, b, c being Element of S holds (w . (a,b)) + (w . (b,c)) = w . (a,c) ) ) );