- commit of the "substitution" component

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cprs_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lift.ma
index 36ce0ef83b4a9d9d9f6d80d78dfa0324089d693f..6298274bc74a5d7813dc0030af5f7df5dd236a70 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lift.ma
@@ -12,67 +12,48 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/reducibility/cpr_lift.ma".
+include "basic_2/reduction/cpr_lift.ma".
 include "basic_2/computation/cprs.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
+(* Advanced properties ******************************************************)
+
+(* Note: apparently this was missing in basic_1 *)
+lemma cprs_delta: ∀G,L,K,V,V2,i.
+                  ⇩[0, i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡* V2 →
+                  ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡* W2.
+#G #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=6/ ]
+#V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
+lapply (ldrop_fwd_drop2 … HLK) -HLK #HLK
+elim (lift_total V1 0 (i+1)) /4 width=11 by cpr_lift, cprs_strap1/
+qed.
+
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_1: was: pr3_gen_lref *)
-lemma cprs_inv_lref1: ∀L,T2,i. L ⊢ #i ➡* T2 →
+lemma cprs_inv_lref1: ∀G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡* T2 →
                       T2 = #i ∨
-                      ∃∃K,V1,T1. ⇩[0, i] L ≡ K. ⓓV1 &
-                                 K ⊢ V1 ➡* T1 &
-                                 ⇧[0, i + 1] T1 ≡ T2 &
-                                 i < |L|.
-#L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1/
+                      ∃∃K,V1,T1. ⇩[0, i] L ≡ K. ⓓV1 & ⦃G, K⦄ ⊢ V1 ➡* T1 &
+                                 ⇧[0, i + 1] T1 ≡ T2.
+#G #L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1/
 #T #T2 #_ #HT2 *
 [ #H destruct
   elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1/
-  * #K #V1 #T1 #HLK #HVT1 #HT12 #Hi
-  @or_intror @(ex4_3_intro … HLK … HT12) // /3 width=3/ (**) (* explicit constructors *)
-| * #K #V1 #T1 #HLK #HVT1 #HT1 #Hi
-  lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
-  elim (cpr_inv_lift1 … H0LK … HT1 … HT2) -H0LK -T /4 width=6/
+  * /4 width=6/
+| * #K #V1 #T1 #HLK #HVT1 #HT1
+  lapply (ldrop_fwd_drop2 … HLK) #H0LK
+  elim (cpr_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T /4 width=6/
 ]
 qed-.
 
-(* Basic_1: was: pr3_gen_abst *)
-lemma cprs_inv_abst1: ∀I,W,a,L,V1,T1,U2. L ⊢ ⓛ{a}V1. T1 ➡* U2 →
-                      ∃∃V2,T2. L ⊢ V1 ➡* V2 & L. ⓑ{I} W ⊢ T1 ➡* T2 &
-                               U2 = ⓛ{a}V2. T2.
-#I #W #a #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /2 width=5/
-#U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
-elim (cpr_inv_abst1 … HU2 I W) -HU2 #V2 #T2 #HV2 #HT2 #H destruct  /3 width=5/
-qed-.
-
-lemma cprs_inv_abst: ∀a,L,V1,V2,T1,T2. L ⊢ ⓛ{a}V1. T1 ➡* ⓛ{a}V2. T2 → ∀I,W.
-                     L ⊢ V1 ➡* V2 ∧ L. ⓑ{I} W ⊢ T1 ➡* T2.
-#a #L #V1 #V2 #T1 #T2 #H #I #W
-elim (cprs_inv_abst1 I W … H) -H #V #T #HV1 #HT1 #H destruct /2 width=1/
-qed-.
-
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was: pr3_lift *)
-lemma cprs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 →
-                 ∀T2. K ⊢ T1 ➡* T2 → ∀U2. ⇧[d, e] T2 ≡ U2 →
-                 L ⊢ U1 ➡* U2.
-#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #HT12 @(cprs_ind … HT12) -T2
-[ -HLK #T2 #HT12
-   <(lift_mono … HTU1 … HT12) -T1 //
-| -HTU1 #T #T2 #_ #HT2 #IHT2 #U2 #HTU2
-  elim (lift_total T d e) #U #HTU
-  lapply (cpr_lift … HLK … HTU … HTU2 … HT2) -T2 -HLK /3 width=3/
-]
-qed.
+lemma cprs_lift: ∀G. l_liftable (cprs G).
+/3 width=9/ qed.
 
 (* Basic_1: was: pr3_gen_lift *)
-lemma cprs_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
-                      ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ➡* U2 →
-                      ∃∃T2. ⇧[d, e] T2 ≡ U2 & K ⊢ T1 ➡* T2.
-#L #K #d #e #HLK #T1 #U1 #HTU1 #U2 #HU12 @(cprs_ind … HU12) -U2 /2 width=3/
--HTU1 #U #U2 #_ #HU2 * #T #HTU #HT1
-elim (cpr_inv_lift1 … HLK … HTU … HU2) -U -HLK /3 width=5/
-qed.
+lemma cprs_inv_lift1: ∀G. l_deliftable_sn (cprs G).
+/3 width=5 by l_deliftable_sn_LTC, cpr_inv_lift1/
+qed-.