reserve x,y,z,a,b,c,X,A for set;
reserve C,D for Coherence_Space;
reserve T for Tolerance of union C;
reserve E for Tolerance of X;

theorem
  CohSp(E) = TolSets E
proof
  thus CohSp(E) c= TolSets E
  proof
    let x be object;
    assume x in CohSp(E);
    then x is TolSet of E by Th14;
    hence thesis by TOLER_1:def 3;
  end;
  let x be object;
  assume x in TolSets E;
  then x is TolSet of E by TOLER_1:def 3;
  hence thesis by Th14;
end;
