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 Lm4p14p1:
  for S being satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              TarskiGeometryStruct
  for a,b,c,a9,b9,c9 being POINT of S st b,a,c cong b9,a9,c9 holds
  a,b,c cong a9,b9,c9
  proof
    let S be satisfying_CongruenceSymmetry
             satisfying_CongruenceEquivalenceRelation
             TarskiGeometryStruct;
    let a,b,c,a9,b9,c9 be POINT of S;
    assume
A1: b,a,c cong b9,a9,c9;
    then a,b equiv b9,a9 by Satz2p4;
    hence a,b,c cong a9,b9,c9 by A1,Satz2p5;
  end;
