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 Th36:
  A is_line & a in A & p in A implies reflection(p,a) in A
  proof
    assume that
A1: A is_line and
A2: a in A and
A3: p in A;
    per cases;
    suppose p = a;
      hence thesis by A2,GTARSKI3:104;
    end;
    suppose
A4:   p <> a;
      Middle a,p,reflection(p,a) by GTARSKI3:def 13;
      then Collinear p,a,reflection(p,a) by GTARSKI4:7;
      then reflection(p,a) in Line(p,a);
      hence thesis by A4,A1,A2,A3,GTARSKI3:87;
    end;
  end;
