for G, F being AbGroup holds
( ( for x being set holds
( x is Element of [:G,F:] iff ex x1 being Element of G ex x2 being Element of F st x = [x1,x2] ) ) & ( for x, y being Element of [:G,F:]
for x1, y1 being Element of G
for x2, y2 being Element of F st x = [x1,x2] & y = [y1,y2] holds
x + y = [(x1 + y1),(x2 + y2)] ) & 0. [:G,F:] = [(0. G),(0. F)] & ( for x being Element of [:G,F:]
for x1 being Element of G
for x2 being Element of F st x = [x1,x2] holds
- x = [(- x1),(- x2)] ) )