 reserve S for satisfying_Tarski-model TarskiGeometryStruct;
 reserve a, b, c, d, e, f, o, p, q, r, s,
    v, w, u, x, y, z, a9, b9, c9, d9, x9, y9, z for POINT of S;

theorem ::: LineEqTrans:
  a <> b & c <> d & e <> f & a,b equal_line c,d & c,d equal_line e,f
    implies a,b equal_line e,f; :::NS
