+(* Basic forward lemmas *****************************************************)
+
+lemma cnv_fwd_flat (a) (h) (I) (G) (L):
+ ∀V,T. ⦃G,L⦄ ⊢ ⓕ{I}V.T ![a,h] →
+ ∧∧ ⦃G,L⦄ ⊢ V ![a,h] & ⦃G,L⦄ ⊢ T ![a,h].
+#a #h * #G #L #V #T #H
+[ elim (cnv_inv_appl … H) #n #p #W #U #_ #HV #HT #_ #_
+| elim (cnv_inv_cast … H) #U #HV #HT #_ #_
+] -H /2 width=1 by conj/
+qed-.
+
+lemma cnv_fwd_pair_sn (a) (h) (I) (G) (L):
+ ∀V,T. ⦃G,L⦄ ⊢ ②{I}V.T ![a,h] → ⦃G,L⦄ ⊢ V ![a,h].
+#a #h * [ #p ] #I #G #L #V #T #H
+[ elim (cnv_inv_bind … H) -H #HV #_
+| elim (cnv_fwd_flat … H) -H #HV #_
+] //
+qed-.
+
+(* Basic_2A1: removed theorems 3: