reserve X for set,
        A for Subset of X,
        R,S for Relation of X;
reserve QUS for Quasi-UniformSpace;
reserve SUS for Semi-UniformSpace;

theorem Th12:
  SUS is empty implies {} in the entourages of SUS
  proof
    assume
A1: SUS is empty;
    assume
A2: not {} in the entourages of SUS;
    SUS is non void;
    then the entourages of SUS is non empty;
    hence thesis by A1,A2;
  end;
