 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 LineEqA1:
  a <> b implies a,b equal_line b,a
   proof
     assume
H1:  a <> b;
     for c holds c on_line a,b iff c on_line b,a by Bsymmetry;
     hence thesis by H1;
   end;
