reserve            S for satisfying_CongruenceSymmetry
                         satisfying_CongruenceEquivalenceRelation
                         TarskiGeometryStruct,
         a,b,c,d,e,f for POINT of S;
reserve S for satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_SAS
              TarskiGeometryStruct,
        q,a,b,c,a9,b9,c9,x1,x2 for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct,
        a,b,c,d for POINT of S;
reserve       S for satisfying_Tarski-model TarskiGeometryStruct,
        a,b,c,d for POINT of S;
reserve         S for satisfying_CongruenceIdentity
                      satisfying_SegmentConstruction
                      satisfying_BetweennessIdentity
                      satisfying_Pasch
                      TarskiGeometryStruct,
        a,b,c,d,e for POINT of S;
reserve       S for satisfying_Tarski-model
                    TarskiGeometryStruct,
      a,b,c,d,p for POINT of S;
reserve                   S for satisfying_Tarski-model TarskiGeometryStruct,
        a,b,c,d,a9,b9,c9,d9 for POINT of S;

theorem Satz4p3:
  between a,b,c & between a9,b9,c9 & a,c equiv a9,c9 & b,c equiv b9,c9
  implies a,b equiv a9,b9
  proof
    assume
A1: between a,b,c & between a9,b9,c9 & a,c equiv a9,c9 & b,c equiv b9,c9;
    then c,a equiv a9,c9 by Satz2p4;
    then a,b,c,a IFS a9,b9,c9,a9 by A1,Satz2p8,Satz2p5;
    then a,b equiv b9,a9 by Satz4p2,Satz2p4;
    hence thesis by Satz2p5;
  end;
