for G, F being non empty addLoopStr holds
( ( for x being set holds
( x is Point of [:G,F:] iff ex x1 being Point of G ex x2 being Point of F st x = [x1,x2] ) ) & ( for x, y being Point of [:G,F:]
for x1, y1 being Point of G
for x2, y2 being Point of F st x = [x1,x2] & y = [y1,y2] holds
x + y = [(x1 + y1),(x2 + y2)] ) & 0. [:G,F:] = [(0. G),(0. F)] ) by Lm1, Def1;