theorem Satz6p2:
  a <> p & b <> p & c <> p & between a,p,c implies
  (between b,p,c iff p out a,b)
  proof
    assume
A1: a <> p & b <> p & c <> p & between a,p,c;
    thus between b,p,c implies p out a,b
    proof
      assume between b,p,c;
      then between c,p,b & between c,p,a by A1,Satz3p2;
      hence thesis by A1,Satz5p2;
    end;
    thus p out a,b implies between b,p,c
    proof
      assume
A2:   p out a,b;
A3:   between p,a,b implies between b,p,c
      proof
        assume between p,a,b;
        then between b,a,p by Satz3p2;
        hence thesis by A1,Satz3p7p1;
      end;
      between p,b,a implies between b,p,c
      proof
        assume between p,b,a;
        then between a,b,p by Satz3p2;
        hence thesis by A1,Satz3p6p1;
      end;
      hence thesis by A2,A3;
    end;
  end;
