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 Th48:
  A is_line & not a in A implies a in Plane(A,a)
  proof
    assume that
A1: A is_line and
A2: not a in A;
    A out a,a & Plane(A,a)
        = {x where x is POINT of S : A out x,a
                                      or x in A
                                      or between a,A,x}
          by A1,A2,Th32,Th17;
    hence a in Plane(A,a);
  end;
