for E, F, G being non empty addLoopStr holds
( ( for x being set holds
( x is Point of [:E,F,G:] iff ex x1 being Point of E ex x2 being Point of F ex x3 being Point of G st x = [x1,x2,x3] ) ) & ( for x1, y1 being Point of E
for x2, y2 being Point of F
for x3, y3 being Point of G holds [x1,x2,x3] + [y1,y2,y3] = [(x1 + y1),(x2 + y2),(x3 + y3)] ) & 0. [:E,F,G:] = [(0. E),(0. F),(0. G)] )