 reserve R for 1-sorted;
 reserve X,Y for Subset of R;
 reserve R for finite 1-sorted;
 reserve X,Y for Subset of R;
 reserve R for finite Approximation_Space;
 reserve X,Y,Z,W for Subset of R;

theorem RIF2Iff:
  for f being satisfying_RIF1 preRIF of R holds
   f is satisfying_RIF2 iff f is satisfying_RIF2*
  proof
    let f be satisfying_RIF1 preRIF of R;
    thus f is satisfying_RIF2 implies f is satisfying_RIF2*
    proof
       assume
A1:    f is satisfying_RIF2;
       let X,Y,Z be Subset of R;
       assume f.(Y,Z) = 1; then
       Y c= Z by RIF1Def;
       hence thesis by A1;
    end;
    assume
A2: f is satisfying_RIF2*;
    let X,Y,Z be Subset of R;
    assume Y c= Z; then
    f.(Y,Z) = 1 by RIF1Def;
    hence thesis by A2;
  end;
