reserve A,X for non empty set;
reserve f for PartFunc of [:X,X:],REAL;
reserve a for Real;

theorem Th38:
  for M being Reflexive symmetric bounded non empty MetrStruct
  st a >= diameter [#]M holds dist_toler(M,a) = dist_toler(M,a)[*]
proof
  let M be Reflexive symmetric bounded non empty MetrStruct such that
A1: a >= diameter [#]M;
  dist_toler(M,a)[*] c= nabla the carrier of M;
  then
  dist_toler(M,a) c= dist_toler(M,a)[*] & dist_toler(M,a)[*] c= dist_toler
  (M,a ) by A1,Th37,LANG1:18;
  hence thesis by XBOOLE_0:def 10;
end;
