reserve S for non empty satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct;
reserve a,b for POINT of S;
reserve A for Subset of S;
reserve S for non empty satisfying_Tarski-model
              TarskiGeometryStruct;
reserve a,b,c,m,r,s for POINT of S;
reserve A for Subset of S;
reserve S         for non empty satisfying_Lower_Dimension_Axiom
                                satisfying_Tarski-model
                                TarskiGeometryStruct,
        a,b,c,d,m,p,q,r,s,x for POINT of S,
        A,A9,E              for Subset of S;

theorem Th61:
  a,a,a,a are_coplanar
  proof
    consider b be POINT of S such that
    between a,a,b and
A1: a <> b by GTARSKI3:36;
    consider c be POINT of S such that
A2: not Collinear a,b,c by A1,GTARSKI3:92;
    consider E be Subset of S such that
    Plane(a,b,c) = E and
A3: E is_plane and
A4: a in E and b in E and c in E by A2,Th49;
    take E;
    thus thesis by A3,A4;
  end;
