normal forms for extended substitution

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cnr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr.ma
index 26bb268eeca5689971b60527c318bb7ed773f577..ad48736fa01d8f0c1f0bc735952e8339c3e77455 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr.ma
@@ -82,6 +82,17 @@ lemma cnr_sort: ∀G,L,k. ⦃G, L⦄ ⊢ ➡ 𝐍⦃⋆k⦄.
 >(cpr_inv_sort1 … H) //
 qed.
 
+lemma cnr_lref_free: ∀G,L,i. |L| ≤ i → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
+#G #L #i #Hi #X #H elim (cpr_inv_lref1 … H) -H // *
+#K #V1 #V2 #HLK lapply (ldrop_fwd_length_lt2 … HLK) -HLK
+#H elim (lt_refl_false i) /2 width=3 by lt_to_le_to_lt/
+qed.
+
+(* Basic_1: was only: nf2_csort_lref *)
+lemma cnr_lref_atom: ∀G,L,i. ⇩[i] L ≡ ⋆ → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
+#G #L #i #HL @cnr_lref_free >(ldrop_fwd_length … HL) -HL //
+qed.
+
 (* Basic_1: was: nf2_abst *)
 lemma cnr_abst: ∀a,G,L,W,T. ⦃G, L⦄ ⊢ ➡ 𝐍⦃W⦄ → ⦃G, L.ⓛW⦄ ⊢ ➡ 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐍⦃ⓛ{a}W.T⦄.
 #a #G #L #W #T #HW #HT #X #H