theorem Lemmapsegcon2:
  ex x being POINT of S st (between p,a,x or between p,x,a) & p,x equiv b,c
  proof
    set q = p;
    consider r be POINT of S such that
A1: between a,q,r & q,r equiv a,q by GTARSKI1:def 8;
    consider x be POINT of S such that
A2: between r,q,x & q,x equiv b,c by GTARSKI1:def 8;
A3: r = q implies ((between q,a,x or between q,x,a) & q,x equiv b,c)
      by A1,A2,Satz2p2,GTARSKI1:def 7;
    r <> q implies ((between q,a,x or between q,x,a) & q,x equiv b,c)
    proof
      assume
A4:   r <> q;
      between r,q,a by A1,Satz3p2;
      hence thesis by A2,A4,Satz5p2;
    end;
    hence thesis by A3;
  end;
