theorem Satz5p1: ::GTARSKI1:37
  a <> b & between a,b,c & between a,b,d implies between a,c,d or between a,d,c
  proof
    assume
A1: a <> b & between a,b,c & between a,b,d;
    then between b,d,c or between b,c,d by GTARSKI1:37;
    hence thesis by A1,Satz3p5p2;
  end;
