
theorem Th1:
  for S being satisfying_CongruenceIdentity
              satisfying_BetweennessIdentity
              TarskiGeometryStruct
  for a,b,c being POINT of S st a,b <= c,c holds a = b
  proof
    let S be satisfying_CongruenceIdentity
             satisfying_BetweennessIdentity
             TarskiGeometryStruct;
    let a,b,c be POINT of S;
    assume a,b <= c,c;
    then consider y be POINT of S such that
A1: between c,y,c and
A2: a,b equiv c,y;
    c = y by A1,GTARSKI1:def 10;
    hence thesis by A2,GTARSKI1:def 7;
  end;
