+
+(* Forward lemmas with strongly rt-normalizing terms ************************)
+
+lemma cnv_fwd_csx (h) (a):
+ ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L❫ ⊢ ⬈*𝐒 T.
+#h #a #G #L #T #H
+/3 width=3 by cnv_fwd_fsb, fsb_inv_csx/
+qed-.
+
+(* Inversion lemmas with proper parallel rst-computation for closures *******)
+
+lemma cnv_fpbg_refl_false (h) (a):
+ ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L,T❫ > ❪G,L,T❫ → ⊥.
+/3 width=7 by cnv_fwd_fsb, fsb_fpbg_refl_false/ qed-.