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

theorem
  (for x st x in X holds neighbourhood(x,R) c= neighbourhood(x,T))
  implies R c= T
proof
  assume
A1: for x st x in X holds neighbourhood(x,R) c= neighbourhood(x,T);
  let x,y be object;
  assume
A2: [x,y] in R;
  then x in X by ZFMISC_1:87;
  then
A3: neighbourhood(x,R) c= neighbourhood(x,T) by A1;
  y in neighbourhood(x,R) by A2,Th27;
  hence thesis by A3,Th27;
end;
