 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 EquivTransitive:
  a,b equiv p,q & p,q equiv r,s implies a,b equiv r,s
  proof
    assume that
X1: a,b equiv p,q and
X2: p,q equiv r,s;
    p,q equiv a,b by X1, EquivSymmetric;
    hence thesis by X2, A2;
  end;
