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;

theorem Satz5p6:
  a,b <= c,d & a,b equiv a9,b9 & c,d equiv c9,d9 implies a9,b9 <= c9,d9
  proof
    assume
A1: a,b <= c,d & a,b equiv a9,b9 & c,d equiv c9,d9;
    then
    consider x be POINT of S such that
A2: between a,b,x & a,x equiv c,d by Satz5p5;
    Collinear a,b,x by A2;
    then consider y be POINT of S such that
A3: a,b,x cong a9,b9,y by A1,Satz4p14;
    a9,y equiv c9,d9
    proof
      a9,y equiv a,x by A3,Satz2p2;
      then a9,y equiv c,d by A2,Satz2p3;
      hence thesis by A1,Satz2p3;
    end;
    hence a9,b9 <= c9,d9 by A2,A3,Satz4p6,Satz5p5;
  end;
