X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcsn_lift.ma;h=5658ab3643f4a8bc5423f55c0962bf84a2f7b13d;hb=82500a9ceb53e1af0263c22afbd5954fa3a83190;hp=14da3109709f4c6afd32c2a8b5460e66fbe33f3a;hpb=e2fd96302d52266bec42a19f100dadc6111fc07b;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma
index 14da31097..5658ab364 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma
@@ -12,77 +12,66 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/reduction/cnf_lift.ma".
+include "basic_2/computation/csn.ma". (**) (* disambiguation error *)
+include "basic_2/reduction/cnx_lift.ma".
 include "basic_2/computation/acp.ma".
-include "basic_2/computation/csn.ma".
 
-(* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
+(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
 
 (* Relocation properties ****************************************************)
 
-(* Basic_1: was: sn3_lift *)
-lemma csn_lift: ∀L2,L1,T1,d,e. L1 ⊢ ⬊* T1 →
-                ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → L2 ⊢ ⬊* T2.
-#L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
+(* Basic_1: was just: sn3_lift *)
+lemma csn_lift: ∀h,g,G,L2,L1,T1,d,e. ⦃G, L1⦄ ⊢ ⬊*[h, g] T1 →
+                ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
+#h #g #G #L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
 @csn_intro #T #HLT2 #HT2
-elim (cpr_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
+elim (cpx_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
 @(IHT1 … HLT10) // -L1 -L2 #H destruct
 >(lift_mono … HT0 … HT12) in HT2; -T1 /2 width=1/
 qed.
 
-(* Basic_1: was: sn3_gen_lift *)
-lemma csn_inv_lift: ∀L2,L1,T1,d,e. L1 ⊢ ⬊* T1 →
-                    ∀T2. ⇩[d, e] L1 ≡ L2 → ⇧[d, e] T2 ≡ T1 → L2 ⊢ ⬊* T2.
-#L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
+(* Basic_1: was just: sn3_gen_lift *)
+lemma csn_inv_lift: ∀h,g,G,L2,L1,T1,d,e. ⦃G, L1⦄ ⊢ ⬊*[h, g] T1 →
+                    ∀T2. ⇩[d, e] L1 ≡ L2 → ⇧[d, e] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
+#h #g #G #L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
 @csn_intro #T #HLT2 #HT2
 elim (lift_total T d e) #T0 #HT0
-lapply (cpr_lift … HLT2 … HL12 … HT21 … HT0) -HLT2 #HLT10
+lapply (cpx_lift … HLT2 … HL12 … HT21 … HT0) -HLT2 #HLT10
 @(IHT1 … HLT10) // -L1 -L2 #H destruct
 >(lift_inj … HT0 … HT21) in HT2; -T1 /2 width=1/
 qed.
 
 (* Advanced properties ******************************************************)
 
-(* Basic_1: was: sn3_abbr *)
-lemma csn_lref_abbr: ∀L,K,V,i. ⇩[0, i] L ≡ K. ⓓV → K ⊢ ⬊* V → L ⊢ ⬊* #i.
-#L #K #V #i #HLK #HV
+(* Basic_1: was just: sn3_abbr *)
+lemma csn_lref_bind: ∀h,g,I,G,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ ⬊*[h, g] V → ⦃G, L⦄ ⊢ ⬊*[h, g] #i.
+#h #g #I #G #L #K #V #i #HLK #HV
 @csn_intro #X #H #Hi
-elim (cpr_inv_lref1 … H) -H
-[ #H destruct elim (Hi ?) //
-| -Hi * #K0 #V0 #V1 #HLK0 #HV01 #HV1
+elim (cpx_inv_lref1 … H) -H
+[ #H destruct elim Hi //
+| -Hi * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HV1
   lapply (ldrop_mono … HLK0 … HLK) -HLK #H destruct
   lapply (ldrop_fwd_ldrop2 … HLK0) -HLK0 #HLK
   @(csn_lift … HLK HV1) -HLK -HV1
-  @(csn_cpr_trans … HV) -HV //
+  @(csn_cpx_trans … HV) -HV //
 ]
 qed.
 
-lemma csn_abst: ∀a,L,W. L ⊢ ⬊* W → ∀I,V,T. L. ⓑ{I} V ⊢ ⬊* T → L ⊢ ⬊* ⓛ{a}W. T.
-#a #L #W #HW elim HW -W #W #_ #IHW #I #V #T #HT @(csn_ind … HT) -T #T #HT #IHT
+lemma csn_appl_simple: ∀h,g,G,L,V. ⦃G, L⦄ ⊢ ⬊*[h, g] V → ∀T1.
+                       (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, g] ⓐV.T2) →
+                       𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬊*[h, g] ⓐV.T1.
+#h #g #G #L #V #H @(csn_ind … H) -V #V #_ #IHV #T1 #IHT1 #HT1
 @csn_intro #X #H1 #H2
-elim (cpr_fwd_abst1 … H1 I V) -H1
-#W0 #T0 #HLW0 #HLT0 #H destruct
-elim (eq_false_inv_tpair_sn … H2) -H2
-[ /3 width=5 by csn_cpr_trans/
-| -HLW0 * #H destruct /3 width=1/
-]
-qed.
-
-lemma csn_appl_simple: ∀L,V. L ⊢ ⬊* V → ∀T1.
-                       (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → L ⊢ ⬊* ⓐV. T2) →
-                       𝐒⦃T1⦄ → L ⊢ ⬊* ⓐV. T1.
-#L #V #H @(csn_ind … H) -V #V #_ #IHV #T1 #IHT1 #HT1
-@csn_intro #X #H1 #H2
-elim (cpr_inv_appl1_simple … H1 ?) // -H1
+elim (cpx_inv_appl1_simple … H1) // -H1
 #V0 #T0 #HLV0 #HLT10 #H destruct
 elim (eq_false_inv_tpair_dx … H2) -H2
 [ -IHV -HT1 #HT10
-  @(csn_cpr_trans … (ⓐV.T0)) /2 width=1/ -HLV0
+  @(csn_cpx_trans … (ⓐV.T0)) /2 width=1/ -HLV0
   @IHT1 -IHT1 // /2 width=1/
 | -HLT10 * #H #HV0 destruct
   @IHV -IHV // -HT1 /2 width=1/ -HV0
   #T2 #HLT02 #HT02
-  @(csn_cpr_trans … (ⓐV.T2)) /2 width=1/ -HLV0
+  @(csn_cpx_trans … (ⓐV.T2)) /2 width=1/ -HLV0
   @IHT1 -IHT1 // -HLT02 /2 width=1/
 ]
 qed.
@@ -90,21 +79,23 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_1: was: sn3_gen_def *)
-lemma csn_inv_lref_abbr: ∀L,K,V,i. ⇩[0, i] L ≡ K. ⓓV → L ⊢ ⬊* #i → K ⊢ ⬊* V.
-#L #K #V #i #HLK #Hi
+lemma csn_inv_lref_bind: ∀h,g,I,G,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V →
+                         ⦃G, L⦄ ⊢ ⬊*[h, g] #i → ⦃G, K⦄ ⊢ ⬊*[h, g] V.
+#h #g #I #G #L #K #V #i #HLK #Hi
 elim (lift_total V 0 (i+1)) #V0 #HV0
 lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
 @(csn_inv_lift … H0LK … HV0) -H0LK
-@(csn_cpr_trans … Hi) -Hi /2 width=6/
+@(csn_cpx_trans … Hi) -Hi /2 width=7/
 qed-.
 
 (* Main properties **********************************************************)
 
-theorem csn_acp: acp cpr (eq …) (csn …).
-@mk_acp
-[ /2 width=1/
-| /2 width=3/
-| /2 width=5/
-| @cnf_lift
+theorem csn_acp: ∀h,g. acp (cpx h g) (eq …) (csn h g).
+#h #g @mk_acp
+[ #G #L elim (deg_total h g 0)
+  #l #Hl lapply (cnx_sort_iter … L … Hl) /2 width=2/
+| @cnx_lift
+| /2 width=3 by csn_fwd_flat_dx/
+| /2 width=1/
 ]
 qed.