Lemma join_symmetry: forall S D a b, joins S D a b -> joins S D b a.
Proof.

move: (H0 x H1) => RC. inversion RC. rewrite -(tm_subst_tm_tm_fresh_eq (open_tm_wrt_tm a2 (a_Var_f x)) a_Bullet x); eauto. rewrite - tm_subst_tm_tm_intro; eauto. move: (fv_tm_tm_tm_open_tm_wrt_tm_lower a2 (a_Var_f x)) => h0. fsetdec. auto. eapply (multipar_iapp _ _ H). eauto. eapply (multipar_iapp _ _ H0). eauto. Unshelve. eauto. eauto. Qed. Lemma multipar_App_destruct_R