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

theorem Th39:
  for M being Reflexive symmetric bounded non empty MetrStruct
  st a >= diameter [#]M holds dist_toler(M,a)[*] = nabla the carrier of M
proof
  let M be Reflexive symmetric bounded non empty MetrStruct such that
A1: a >= diameter [#]M;
  dist_toler(M,a) = dist_toler(M,a)[*] by A1,Th38;
  hence thesis by A1,Th37;
end;
