theorem
  r <> a & b <> c implies ex x being POINT of S st (a out x,r & a,x equiv b,c)
  proof
    assume
A1: r <> a & b <> c;
    consider x be POINT of S such that
A2: (between a,r,x or between a,x,r) & a,x equiv b,c by Lemmapsegcon2;
    a out x,r by A1,A2,Satz2p2,GTARSKI1:def 7;
    hence thesis by A2;
  end;
