reserve X for set,
        D for a_partition of X,
        TG for non empty TopologicalGroup;
reserve A for Subset of X;
reserve US for UniformSpace;
reserve R for Relation of X;

theorem Th25:
  for X being set,R being total reflexive Relation of X holds
    uniformity_induced_by(R) is axiom_U1
  proof
    let X be set, R be total reflexive Relation of X;
    rho(R) is axiom_UP1 by Th21;
    hence thesis;
  end;
