reserve X,Y,Z,x,y,z for set;
reserve T,R for Tolerance of X;

theorem
  for Y,Z st Y is TolSet of T holds Y /\ Z is TolSet of T
proof
  let Y,Z such that
A1: Y is TolSet of T;
  let x,y;
  assume x in Y /\ Z & y in Y /\ Z;
  then x in Y & y in Y by XBOOLE_0:def 4;
  hence thesis by A1,Def1;
end;
