X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpxs_drops.ma;h=c42f94f83b665ee43394297b61cda43a7aa5fd6a;hp=08eed14817d6884a829c9b23f6577959803853cc;hb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;hpb=65383ff6ec2236b0a61310b872ea4cd5fcc26fb7

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
index 08eed1481..c42f94f83 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
@@ -12,52 +12,43 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/drops_lstar.ma".
+include "static_2/relocation/drops_ctc.ma".
 include "basic_2/rt_transition/cpx_drops.ma".
 include "basic_2/rt_computation/cpxs.ma".
 
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
 (* Advanced properties ******************************************************)
 
 lemma cpxs_delta: ∀h,I,G,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈*[h] V2 →
-                  ∀W2. ⬆*[1] V2 ≡ W2 → ⦃G, K.ⓑ{I}V1⦄ ⊢ #0 ⬈*[h] W2.
+                  ∀W2. ⬆*[1] V2 ≘ W2 → ⦃G, K.ⓑ{I}V1⦄ ⊢ #0 ⬈*[h] W2.
 #h #I #G #K #V1 #V2 #H @(cpxs_ind … H) -V2
 [ /3 width=3 by cpx_cpxs, cpx_delta/
 | #V #V2 #_ #HV2 #IH #W2 #HVW2
-  elim (lifts_total V (𝐔❴1❵)) #W #HVW
-  elim (cpx_lifts … HV2 (Ⓣ) … (K.ⓑ{I}V1) … HVW) -HV2
-  [ #V0 #HV20 <(lifts_mono … HVW2 … HV20) -V2 -V0 /3 width=3 by cpxs_strap1/
-  | /3 width=1 by drops_refl, drops_drop/
-  ]
+  elim (lifts_total V (𝐔❴1❵))
+  /5 width=11 by cpxs_strap1, cpx_lifts_bi, drops_refl, drops_drop/
 ]
 qed.
 
-lemma cpxs_lref: ∀h,I,G,K,V,T,i. ⦃G, K⦄ ⊢ #i ⬈*[h] T →
-                 ∀U. ⬆*[1] T ≡ U → ⦃G, K.ⓑ{I}V⦄ ⊢ #⫯i ⬈*[h] U.
-#h #I #G #K #V #T #i #H @(cpxs_ind … H) -T
+lemma cpxs_lref: ∀h,I,G,K,T,i. ⦃G, K⦄ ⊢ #i ⬈*[h] T →
+                 ∀U. ⬆*[1] T ≘ U → ⦃G, K.ⓘ{I}⦄ ⊢ #↑i ⬈*[h] U.
+#h #I #G #K #T #i #H @(cpxs_ind … H) -T
 [ /3 width=3 by cpx_cpxs, cpx_lref/
 | #T0 #T #_ #HT2 #IH #U #HTU
-  elim (lifts_total T0 (𝐔❴1❵)) #U0 #HTU0
-  elim (cpx_lifts … HT2 (Ⓣ) … (K.ⓑ{I}V) … HTU0) -HT2
-  [ #X #HTX <(lifts_mono … HTU … HTX) -T -X /3 width=3 by cpxs_strap1/
-  | /3 width=1 by drops_refl, drops_drop/
-  ]
+  elim (lifts_total T0 (𝐔❴1❵))
+  /5 width=11 by cpxs_strap1, cpx_lifts_bi, drops_refl, drops_drop/
 ]
 qed.
 
 (* Basic_2A1: was: cpxs_delta *)
 lemma cpxs_delta_drops: ∀h,I,G,L,K,V1,V2,i.
-                        ⬇*[i] L ≡ K.ⓑ{I}V1 → ⦃G, K⦄ ⊢ V1 ⬈*[h] V2 →
-                        ∀W2. ⬆*[⫯i] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ⬈*[h] W2.
+                        ⬇*[i] L ≘ K.ⓑ{I}V1 → ⦃G, K⦄ ⊢ V1 ⬈*[h] V2 →
+                        ∀W2. ⬆*[↑i] V2 ≘ W2 → ⦃G, L⦄ ⊢ #i ⬈*[h] W2.
 #h #I #G #L #K #V1 #V2 #i #HLK #H @(cpxs_ind … H) -V2
 [ /3 width=7 by cpx_cpxs, cpx_delta_drops/
 | #V #V2 #_ #HV2 #IH #W2 #HVW2
-  elim (lifts_total V (𝐔❴⫯i❵)) #W #HVW
-  elim (cpx_lifts … HV2 (Ⓣ) … L … HVW) -HV2
-  [ #V0 #HV20 <(lifts_mono … HVW2 … HV20) -V2 -V0 /3 width=3 by cpxs_strap1/
-  | /2 width=3 by drops_isuni_fwd_drop2/
-  ]
+  elim (lifts_total V (𝐔❴↑i❵))
+  /4 width=11 by cpxs_strap1, cpx_lifts_bi, drops_isuni_fwd_drop2/
 ]
 qed.
 
@@ -65,7 +56,7 @@ qed.
 
 lemma cpxs_inv_zero1: ∀h,G,L,T2. ⦃G, L⦄ ⊢ #0 ⬈*[h] T2 →
                       T2 = #0 ∨
-                      ∃∃I,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈*[h] V2 & ⬆*[1] V2 ≡ T2 &
+                      ∃∃I,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈*[h] V2 & ⬆*[1] V2 ≘ T2 &
                                    L = K.ⓑ{I}V1.
 #h #G #L #T2 #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
@@ -73,30 +64,30 @@ lemma cpxs_inv_zero1: ∀h,G,L,T2. ⦃G, L⦄ ⊢ #0 ⬈*[h] T2 →
   elim (cpx_inv_zero1 … HT2) -HT2 /2 width=1 by or_introl/
   * /4 width=7 by cpx_cpxs, ex3_4_intro, or_intror/
 | * #I #K #V1 #T1 #HVT1 #HT1 #H destruct
-  elim (cpx_inv_lifts … HT2 (Ⓣ) … K … HT1) -T
+  elim (cpx_inv_lifts_sn … HT2 (Ⓣ) … K … HT1) -T
   /4 width=7 by cpxs_strap1, drops_refl, drops_drop, ex3_4_intro, or_intror/
 ]
 qed-.
 
-lemma cpxs_inv_lref1: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ⬈*[h] T2 →
-                      T2 = #(⫯i) ∨
-                      ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ⬈*[h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V.
+lemma cpxs_inv_lref1: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #↑i ⬈*[h] T2 →
+                      T2 = #(↑i) ∨
+                      ∃∃I,K,T. ⦃G, K⦄ ⊢ #i ⬈*[h] T & ⬆*[1] T ≘ T2 & L = K.ⓘ{I}.
 #h #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
   elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
-  * /4 width=7 by cpx_cpxs, ex3_4_intro, or_intror/
-| * #I #K #V1 #T1 #Hi #HT1 #H destruct
-  elim (cpx_inv_lifts … HT2 (Ⓣ) … K … HT1) -T
-  /4 width=7 by cpxs_strap1, drops_refl, drops_drop, ex3_4_intro, or_intror/
+  * /4 width=6 by cpx_cpxs, ex3_3_intro, or_intror/
+| * #I #K #T1 #Hi #HT1 #H destruct
+  elim (cpx_inv_lifts_sn … HT2 (Ⓣ) … K … HT1) -T
+  /4 width=6 by cpxs_strap1, drops_refl, drops_drop, ex3_3_intro, or_intror/
 ]
 qed-.
 
 (* Basic_2A1: was: cpxs_inv_lref1 *)
 lemma cpxs_inv_lref1_drops: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ⬈*[h] T2 →
                             T2 = #i ∨
-                            ∃∃I,K,V1,T1. ⬇*[i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ⬈*[h] T1 &
-                                         ⬆*[⫯i] T1 ≡ T2.
+                            ∃∃I,K,V1,T1. ⬇*[i] L ≘ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ⬈*[h] T1 &
+                                         ⬆*[↑i] T1 ≘ T2.
 #h #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
@@ -104,7 +95,7 @@ lemma cpxs_inv_lref1_drops: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ⬈*[h] T2 →
   * /4 width=7 by cpx_cpxs, ex3_4_intro, or_intror/
 | * #I #K #V1 #T1 #HLK #HVT1 #HT1
   lapply (drops_isuni_fwd_drop2 … HLK) // #H0LK
-  elim (cpx_inv_lifts … HT2 … H0LK … HT1) -H0LK -T
+  elim (cpx_inv_lifts_sn … HT2 … H0LK … HT1) -H0LK -T
   /4 width=7 by cpxs_strap1, ex3_4_intro, or_intror/
 ]
 qed-.
@@ -112,11 +103,17 @@ qed-.
 (* Properties with generic relocation ***************************************)
 
 (* Basic_2A1: includes: cpxs_lift *)
-lemma cpxs_lifts: ∀h,G. d_liftable2 (cpxs h G).
-/3 width=10 by cpx_lifts, cpxs_strap1, d2_liftable_LTC/ qed-.
+lemma cpxs_lifts_sn: ∀h,G. d_liftable2_sn … lifts (cpxs h G).
+/3 width=10 by cpx_lifts_sn, cpxs_strap1, d2_liftable_sn_CTC/ qed-.
+
+lemma cpxs_lifts_bi: ∀h,G. d_liftable2_bi … lifts (cpxs h G).
+/3 width=12 by cpxs_lifts_sn, d_liftable2_sn_bi, lifts_mono/ qed-.
 
 (* Inversion lemmas with generic relocation *********************************)
 
 (* Basic_2A1: includes: cpxs_inv_lift1 *)
-lemma cpxs_inv_lifts: ∀h,G. d_deliftable2_sn (cpxs h G).
-/3 width=6 by d2_deliftable_sn_LTC, cpx_inv_lifts/ qed-.
+lemma cpxs_inv_lifts_sn: ∀h,G. d_deliftable2_sn … lifts (cpxs h G).
+/3 width=6 by d2_deliftable_sn_CTC, cpx_inv_lifts_sn/ qed-.
+
+lemma cpxs_inv_lifts_bi: ∀h,G. d_deliftable2_bi … lifts (cpxs h G).
+/3 width=12 by cpxs_inv_lifts_sn, d_deliftable2_sn_bi, lifts_inj/ qed-.