for g being ConwayGame holds
( ( for x being set holds
( x in the_LeftOptions_of (- g) iff ex gR being ConwayGame st
( gR in the_RightOptions_of g & x = - gR ) ) ) & ( for x being set holds
( x in the_RightOptions_of (- g) iff ex gL being ConwayGame st
( gL in the_LeftOptions_of g & x = - gL ) ) ) )