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;
reserve S for satisfying_Tarski-model
              TarskiGeometryStruct,
        a,b,c,d,a9,b9,c9,d9,p,q for POINT of S;
reserve                       S for satisfying_Tarski-model
                                    TarskiGeometryStruct,
        a,b,c,d,e,f,a9,b9,c9,d9 for POINT of S;
reserve p for POINT of S;
reserve r for POINT of S;
reserve x,y for POINT of S;
reserve S for non empty satisfying_Tarski-model TarskiGeometryStruct;
reserve p,q,r,s for POINT of S;
reserve S for non empty satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct,
  a,b,p,q for POINT of S;
reserve S for non empty satisfying_Tarski-model TarskiGeometryStruct,
                  A,B for Subset of S,
        a,b,c,p,q,r,s for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct,
        a,b,m for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              TarskiGeometryStruct,
        a,b,m for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_SegmentConstruction
              satisfying_SAS
              TarskiGeometryStruct,
        a for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_SAS
              TarskiGeometryStruct,
  a,p,p9 for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_SAS
              satisfying_Pasch
              TarskiGeometryStruct,
  a,p,p9 for POINT of S;
reserve S for satisfying_CongruenceIdentity
                satisfying_CongruenceSymmetry
                satisfying_CongruenceEquivalenceRelation
                satisfying_SegmentConstruction
                satisfying_BetweennessIdentity
                satisfying_SAS
                TarskiGeometryStruct,
        a,p for POINT of S;
reserve              S for satisfying_Tarski-model TarskiGeometryStruct,
        a,b,c,d,m,p,p9,q,r,s for POINT of S;

theorem Satz7p17:
  Middle p,a,p9 & Middle p,b,p9 implies a = b
  proof
    assume that
A1: Middle p,a,p9 and
A2: Middle p,b,p9;
    now
      thus between p,b,p9 by A2;
      reflection(a,p) = p9 by A1,DEFR;
      then b,p9 equiv reflection(a,b),reflection(a,reflection(a,p))
        by Satz7p13;
      then b,p9 equiv reflection(a,b),p by Satz7p7;
      then b,p equiv reflection(a,b),p by A2,Satz2p3;
      hence p,b equiv reflection(a,b),p by Satz2p4;
      hence p,b equiv p,reflection(a,b) by Satz2p5;
      b,p equiv reflection(a,b),reflection(a,p) by Satz7p13;
      then b,p equiv reflection(a,b),p9 by A1,DEFR;
      then b,p9 equiv reflection(a,b),p9 by A2,GTARSKI1:def 6;
      then p9,b equiv reflection(a,b),p9 by Satz2p4;
      hence p9,b equiv p9,reflection(a,b) by Satz2p5;
    end;
    then reflection(a,b) = b by Satz4p19;
    hence thesis by Satz7p10;
  end;
