for G being non empty right_complementable Abelian add-associative right_zeroed midpoint_operator addLoopStr
for M being non empty MidStr
for w being Function of [: the carrier of M, the carrier of M:], the carrier of G
for a, b, c being Point of M st w is_atlas_of the carrier of M,G & w is associating holds
( a @ c = b iff w . (a,c) = Double (w . (a,b)) )