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
  a,b,c,d are_coplanar implies a,b,d,c are_coplanar &
  a,c,b,d are_coplanar & a,c,d,b are_coplanar &
  a,d,c,b are_coplanar & a,d,b,c are_coplanar &
  b,a,c,d are_coplanar & b,a,d,c are_coplanar &
  b,c,a,d are_coplanar & b,c,d,a are_coplanar &
  b,d,a,c are_coplanar & b,d,c,a are_coplanar &
  c,a,b,d are_coplanar & c,a,d,b are_coplanar &
  c,b,a,d are_coplanar & c,b,d,a are_coplanar &
  d,a,b,c are_coplanar & d,a,c,b are_coplanar &
  d,b,a,c are_coplanar & d,b,c,a are_coplanar;
