:: deftheorem Def1 defines dist_cart2 METRIC_3:def 1 :
for X, Y being non empty MetrSpace
for b₃ being Function of [:[: the carrier of X, the carrier of Y:],[: the carrier of X, the carrier of Y:]:],REAL holds
( b₃ = dist_cart2 (X,Y) iff for x1, y1 being Element of X
for x2, y2 being Element of Y
for x, y being Element of [: the carrier of X, the carrier of Y:] st x = [x1,x2] & y = [y1,y2] holds
b₃ . (x,y) = (dist (x1,y1)) + (dist (x2,y2)) );