theorem Lemma5p12p4:
  between a,c,b & a,b <= a,c implies b = c
  proof
    assume
A1: between a,c,b & a,b <= a,c;
    then consider x be POINT of S such that
A2: between a,b,x & a,x equiv a,c by Satz5p5;
    c = x by A1,A2,Lemma5p12p3,Satz3p6p2;
    hence thesis by A1,A2,Satz3p6p1,GTARSKI1:def 10;
  end;
