:: deftheorem defines is_metric_of PCOMPS_1:def 6 :
for D being set
for f being Function of [:D,D:],REAL holds
( f is_metric_of D iff for a, b, c being Element of D holds
( ( f . (a,b) = 0 implies a = b ) & ( a = b implies f . (a,b) = 0 ) & f . (a,b) = f . (b,a) & f . (a,c) <= (f . (a,b)) + (f . (b,c)) ) );