theorem Satz4p6:
  between a,b,c & a,b,c cong a9,b9,c9 implies between a9,b9,c9
  proof
    assume
A1: between a,b,c & a,b,c cong a9,b9,c9;
    consider b99 be POINT of S such that
A3: between a9,b99,c9 & a,b,c cong a9,b99,c9 by A1,Satz4p5;
A5: a9,b99 equiv a,b & b99,c9 equiv b,c by A3,Satz2p2;
    then a9,b99 equiv a9,b9 & b99,c9 equiv b9,c9 by A1,Satz2p3;
    then c9,b99 equiv b9,c9 by Satz2p4;
    then a9,b99,c9,b99 IFS a9,b99,c9,b9 by A5,A3,A1,Satz2p1,Satz2p3,Satz2p5;
    then b99,b9 equiv b99,b99 by Satz2p2,Satz4p2;
    hence thesis by A3,GTARSKI1:def 7;
  end;
