:: deftheorem Def8 defines fam_class_metr TAXONOM1:def 8 :
for M being non empty Reflexive symmetric MetrStruct
for b₂ being Subset of (PARTITIONS the carrier of M) holds
( b₂ = fam_class_metr M iff for x being object holds
( x in b₂ iff ex a being non negative Real ex R being Equivalence_Relation of M st
( R = (dist_toler (M,a)) [*] & Class R = x ) ) );