Hint Extern 1 (lc_co (g_AbsCong _ _ _)) =>
  let x1 := fresh in
  pick_fresh x1;
  apply (lc_g_AbsCong_exists x1).Hint Extern 1 (lc_co (g_CAbsCong _ _ _)) =>
  let c1 := fresh in
  pick_fresh c1;
  apply (lc_g_CAbsCong_exists c1).

Lemma tm_subst_tm_constraint_open_constraint_wrt_tm_var : forall phi1 a1 x1 x2, x1 <> x2 -> lc_tm a1 -> open_constraint_wrt_tm (tm_subst_tm_constraint a1 x1 phi1) (a_Var_f x2) = tm_subst_tm_constraint a1 x1 (open_constraint_wrt_tm phi1 (a_Var_f x2)).