 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 Baaa:
  between a,a,a & a,a equiv b,b
  proof
    consider x such that
Z1: between a,a,x & a,x equiv b,b by A4;
    thus between a,a,a & a,a equiv b,b by Z1, A3;
  end;
