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+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "Basic_2/substitution/lift_vector.ma".
+include "Basic_2/computation/cprs_tstc.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
+
+(* Vector form of forward lemmas involving same top term constructor ********)
+
+lemma cpr_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
+ ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡ U →
+ ⒶV1s. ⓓV. T ≃ U ∨ L ⊢ ⓓV. ⒶV2s. T ➡* U.
+#L #V1s #V2s * -V1s -V2s /3 width=1/
+#V1s #V2s #V1a #V2a #HV12a * -V1s -V2s /2 width=1 by cpr_fwd_theta/ -HV12a
+#V1s #V2s #V1b #V2b #_ #_ #V #U #T #H
+elim (cpr_inv_appl1_simple … H ?) -H //
+#V0 #T0 #_ #_ #H destruct /2 width=1/
+qed-.
+
+axiom cprs_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
+ ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡* U →
+ ⒶV1s. ⓓV. T ≃ U ∨ L ⊢ ⓓV. ⒶV2s. T ➡* U.
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