theorem Th78:
  for t, u, v, w st t LD-= u & v LD-= w holds t '=' v LD-= u '=' w
proof
  deffunc F( GRZ-formula, GRZ-formula ) = $1 '=' $2;
  defpred P[ GRZ-formula, GRZ-formula ] means $1 '=' $2 is LD-provable;
  A2: for t, u, v st P[t, u] & P[u, v] holds P[t, v] by Th74;
  A3: for t, u holds P[F(t,u), F(u,t)];
  A4: for t, u, v st P[t, u] holds P[F(t,v), F(u,v)] by Lm78a;
  for t, u, v, w st P[t, u] & P[v, w] holds P[F(t, v), F(u, w)]
      from BinReplace(A2, A3, A4);
  hence thesis;
end;
