(* Vector form of forward lemmas involving same top term constructor ********)
-lemma cprs_fwd_cnf_vector: ∀L,T. 𝐒[T] → L ⊢ 𝐍[T] → ∀Vs,U. L ⊢ ⒶVs.T ➡* U → ⒶVs.T ≃ U.
+(* Basic_1: was just: nf2_iso_appls_lref *)
+lemma cprs_fwd_cnf_vector: ∀L,T. 𝐒⦃T⦄ → L ⊢ 𝐍⦃T⦄ → ∀Vs,U. L ⊢ ⒶVs.T ➡* U → ⒶVs.T ≃ U.
#L #T #H1T #H2T #Vs elim Vs -Vs [ @(cprs_fwd_cnf … H2T) ] (**) (* /2 width=3 by cprs_fwd_cnf/ does not work *)
#V #Vs #IHVs #U #H
elim (cprs_inv_appl1 … H) -H *
qed-.
(* Basic_1: was: pr3_iso_appls_cast *)
-lemma cprs_fwd_tau_vector: â\88\80L,Vs,W,T,U. L â\8a¢ â\92¶Vs. â\93£W. T ➡* U →
- â\92¶Vs. â\93£W. T ≃ U ∨ L ⊢ ⒶVs. T ➡* U.
+lemma cprs_fwd_tau_vector: â\88\80L,Vs,W,T,U. L â\8a¢ â\92¶Vs. â\93\9dW. T ➡* U →
+ â\92¶Vs. â\93\9dW. T ≃ U ∨ L ⊢ ⒶVs. T ➡* U.
#L #Vs elim Vs -Vs /2 width=1 by cprs_fwd_tau/
#V #Vs #IHVs #W #T #U #H
elim (cprs_inv_appl1 … H) -H *