theorem
  for S being satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              TarskiGeometryStruct holds
  S is satisfying_SAS iff S is (FS)
  proof
    let S be satisfying_CongruenceSymmetry
             satisfying_CongruenceEquivalenceRelation
             TarskiGeometryStruct;
    hereby
      assume S is satisfying_SAS;
      then S is satisfying_SST_A5;
      hence S is (FS);
    end;
    assume S is (FS);
    then S is satisfying_SST_A5;
    hence S is satisfying_SAS;
  end;
