universary milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr_lift.ma
index 8d0267c474b17b44f66d182aab5946030902827a..eef9aefc873c3441c286a999cde559b412fd6c9c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr_lift.ma
@@ -15,43 +15,35 @@
 include "basic_2/reduction/cpr_lift.ma".
 include "basic_2/reduction/cnr.ma".
 
-(* CONTEXT-SENSITIVE NORMAL TERMS *******************************************)
+(* NORMAL TERMS FOR CONTEXT-SENSITIVE REDUCTION *****************************)
 
 (* Advanced properties ******************************************************)
 
-(* Basic_1: was only: nf2_csort_lref *)
-lemma cnr_lref_atom: ∀L,i. ⇩[0, i] L ≡ ⋆ → ⦃G, L⦄ ⊢ 𝐍⦃#i⦄.
-#L #i #HL #X #H
-elim (cpr_inv_lref1 … H) -H // *
-#K #V1 #V2 #HLK #_ #_
-lapply (ldrop_mono … HL … HLK) -L #H destruct
-qed.
-
 (* Basic_1: was: nf2_lref_abst *)
-lemma cnr_lref_abst: ∀L,K,V,i. ⇩[0, i] L ≡ K. ⓛV → ⦃G, L⦄ ⊢ 𝐍⦃#i⦄.
-#L #K #V #i #HLK #X #H
+lemma cnr_lref_abst: ∀G,L,K,V,i. ⬇[i] L ≡ K. ⓛV → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
+#G #L #K #V #i #HLK #X #H
 elim (cpr_inv_lref1 … H) -H // *
 #K0 #V1 #V2 #HLK0 #_ #_
-lapply (ldrop_mono … HLK … HLK0) -L #H destruct
+lapply (drop_mono … HLK … HLK0) -L #H destruct
 qed.
 
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was: nf2_lift *)
-lemma cnr_lift: ∀L0,L,T,T0,d,e.
-                â¦\83G, Lâ¦\84 â\8a¢ ð\9d\90\8dâ¦\83Tâ¦\84 â\86\92 â\87©[d, e] L0 â\89¡ L â\86\92 â\87§[d, e] T â\89¡ T0 â\86\92 L0 â\8a¢ 𝐍⦃T0⦄.
-#L0 #L #T #T0 #d #e #HLT #HL0 #HT0 #X #H
+lemma cnr_lift: ∀G,L0,L,T,T0,c,l,k. ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ →
+                â¬\87[c, l, k] L0 â\89¡ L â\86\92 â¬\86[l, k] T â\89¡ T0 â\86\92 â¦\83G, L0â¦\84 â\8a¢ â\9e¡ 𝐍⦃T0⦄.
+#G #L0 #L #T #T0 #c #l #k #HLT #HL0 #HT0 #X #H
 elim (cpr_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
 <(HLT … HT1) in HT0; -L #HT0
 >(lift_mono … HT10 … HT0) -T1 -X //
 qed.
 
 (* Note: this was missing in basic_1 *)
-lemma cnr_inv_lift: ∀L0,L,T,T0,d,e.
-                    L0 ⊢ 𝐍⦃T0⦄ → ⇩[d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → ⦃G, L⦄ ⊢ 𝐍⦃T⦄.
-#L0 #L #T #T0 #d #e #HLT0 #HL0 #HT0 #X #H
-elim (lift_total X d e) #X0 #HX0
+lemma cnr_inv_lift: ∀G,L0,L,T,T0,c,l,k. ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄ →
+                    ⬇[c, l, k] L0 ≡ L → ⬆[l, k] T ≡ T0 → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
+#G #L0 #L #T #T0 #c #l #k #HLT0 #HL0 #HT0 #X #H
+elim (lift_total X l k) #X0 #HX0
 lapply (cpr_lift … H … HL0 … HT0 … HX0) -L #HTX0
 >(HLT0 … HTX0) in HX0; -L0 -X0 #H
->(lift_inj … H … HT0) -T0 -X -d -e //
+>(lift_inj … H … HT0) -T0 -X -c -l -k //
 qed-.