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 Th14:
  a in CohSp(E) iff a is TolSet of E
proof
  thus a in CohSp(E) implies a is TolSet of E
  proof
    assume a in CohSp(E);
    then for x,y st x in a & y in a holds [x,y] in E by Def3;
    hence thesis by TOLER_1:def 1;
  end;
  assume a is TolSet of E;
  then for x,y st x in a & y in a holds [x,y] in E by TOLER_1:def 1;
  hence thesis by Def3;
end;
