-fact csnv_inv_cons_aux: ∀L,Ts. L ⊢ ⬇* Ts → ∀U,Us. Ts = U :: Us →
- L ⊢ ⬇* U ∧ L ⊢ ⬇* Us.
-#L #Ts * -Ts
-[ #U #Us #H destruct
-| #Ts #T #HT #HTs #U #Us #H destruct /2 width=1/
-]
-qed.
-
-lemma csnv_inv_cons: ∀L,T,Ts. L ⊢ ⬇* T :: Ts → L ⊢ ⬇* T ∧ L ⊢ ⬇* Ts.
-/2 width=3/ qed-.
-
-include "basic_2/computation/csn_cpr.ma".
-
-lemma csn_fwd_applv: ∀L,T,Vs. L ⊢ ⬇* Ⓐ Vs. T → L ⊢ ⬇* Vs ∧ L ⊢ ⬇* T.
-#L #T #Vs elim Vs -Vs /2 width=1/
-#V #Vs #IHVs #HVs
-lapply (csn_fwd_pair_sn … HVs) #HV
-lapply (csn_fwd_flat_dx … HVs) -HVs #HVs
-elim (IHVs HVs) -IHVs -HVs /3 width=1/
-qed-.