for E, F, G being RealNormSpace 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)] & ( for x1 being Point of E
for x2 being Point of F
for x3 being Point of G
for a being Real holds a * [x1,x2,x3] = [(a * x1),(a * x2),(a * x3)] ) & ( for x1 being Point of E
for x2 being Point of F
for x3 being Point of G holds - [x1,x2,x3] = [(- x1),(- x2),(- x3)] ) & ( for x1 being Point of E
for x2 being Point of F
for x3 being Point of G holds
( ||.[x1,x2,x3].|| = sqrt (((||.x1.|| ^2) + (||.x2.|| ^2)) + (||.x3.|| ^2)) & ex w being Element of REAL 3 st
( w = <*||.x1.||,||.x2.||,||.x3.||*> & ||.[x1,x2,x3].|| = |.w.| ) ) ) )