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;

theorem Satz3p1: ::Bqaa
  for S being satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              TarskiGeometryStruct
  for a,b being POINT of S holds between a,b,b
  proof
    let S be satisfying_CongruenceIdentity
             satisfying_SegmentConstruction
             TarskiGeometryStruct;
    let a,b be POINT of S;
    ex x be POINT of S st between a,b,x & b,x equiv b,b by GTARSKI1:def 8;
    hence thesis by GTARSKI1:def 7;
  end;
