+(* Basic forward lemmas *****************************************************)
+
+lemma cpr_fwd_shift1: ∀L,L1,T1,T. L ⊢ L1 @@ T1 ➡ T →
+ ∃∃L2,T2. |L1| = |L2| & T = L2 @@ T2.
+#L #L1 #T1 #T * #X #H1 #H2
+elim (tpr_fwd_shift1 … H1) -H1 #L0 #T0 #HL10 #H destruct
+elim (tpss_fwd_shift1 … H2) -H2 #L2 #T2 #HL02 #H destruct /2 width=4/
+qed-.
+