X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Faaa_drops.ma;h=930ca157c9338e84451229761fc26ba0a3785ee9;hp=5ef58ee9f1bbeb91c7a88d72ff30055813af0624;hb=222044da28742b24584549ba86b1805a87def070;hpb=3ef251397627da80aeea0cf08b053a4bc781ef88

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_drops.ma
index 5ef58ee9f..930ca157c 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_drops.ma
@@ -22,55 +22,57 @@ include "basic_2/static/aaa.ma".
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: was: aaa_lref *)
-lemma aaa_lref_gen: ∀I,G,K,V,B,i,L. ⬇*[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ⁝ B → ⦃G, L⦄ ⊢ #i ⁝ B.
+lemma aaa_lref_drops: ∀I,G,K,V,B,i,L. ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ⁝ B → ⦃G, L⦄ ⊢ #i ⁝ B.
 #I #G #K #V #B #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H //
   #H destruct /2 width=1 by aaa_zero/
-| #i #IH #L <uni_succ #H #HB lapply (drops_inv_pair2_isuni_next … H) -H // *
-  #Z #Y #X #HY #H destruct /3 width=1 by aaa_lref/
+| #i #IH #L <uni_succ #H #HB lapply (drops_inv_bind2_isuni_next … H) -H // *
+  #Z #Y #HY #H destruct /3 width=1 by aaa_lref/
 ]
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_2A1: was: aaa_inv_lref *)
-lemma aaa_inv_lref_gen: ∀G,A,i,L. ⦃G, L⦄ ⊢ #i ⁝ A →
-                        ∃∃I,K,V. ⬇*[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ⁝ A.
+lemma aaa_inv_lref_drops: ∀G,A,i,L. ⦃G, L⦄ ⊢ #i ⁝ A →
+                          ∃∃I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ⁝ A.
 #G #A #i elim i -i
 [ #L #H elim (aaa_inv_zero … H) -H /3 width=5 by drops_refl, ex2_3_intro/
 | #i #IH #L #H elim (aaa_inv_lref … H) -H
-  #I #K #V #H #HA destruct elim (IH … HA) -IH -HA /3 width=5 by drops_drop, ex2_3_intro/
+  #I #K #H #HA destruct elim (IH … HA) -IH -HA /3 width=5 by drops_drop, ex2_3_intro/
 ]
 qed-.
 
 (* Properties with generic slicing for local environments *******************)
 
 (* Basic_2A1: includes: aaa_lift *)
-lemma aaa_lifts: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀L2,c,f. ⬇*[c, f] L2 ≡ L1 →
-                 ∀T2. ⬆*[f] T1 ≡ T2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
-@fqup_wf_ind_eq #G0 #L0 #T0 #IH #G #L1 * *
-[ #s #HG #HL #HT #A #H #L2 #c #f #HL21 #X #HX -IH -c
+(* Note: it should use drops_split_trans_pair2 *)
+lemma aaa_lifts: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀b,f,L2. ⬇*[b, f] L2 ≘ L1 →
+                 ∀T2. ⬆*[f] T1 ≘ T2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
+@(fqup_wf_ind_eq (Ⓣ)) #G0 #L0 #T0 #IH #G #L1 * *
+[ #s #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX -b -IH
   lapply (aaa_inv_sort … H) -H #H destruct
   >(lifts_inv_sort1 … HX) -HX //
-| #i1 #HG #HL #HT #A #H #L2 #c #f #HL21 #X #HX
-  elim (aaa_inv_lref_gen … H) -H #J #K1 #V1 #HLK1 #HA
+| #i1 #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX
+  elim (aaa_inv_lref_drops … H) -H #J #K1 #V1 #HLK1 #HA
   elim (lifts_inv_lref1 … HX) -HX #i2 #Hf #H destruct
   lapply (drops_trans … HL21 … HLK1 ??) -HL21 [1,2: // ] #H
   elim (drops_split_trans … H) -H [ |*: /2 width=6 by after_uni_dx/ ] #Y #HLK2 #HY
-  lapply (drops_inv_tls_at … Hf … HY) -HY #HY -Hf
-  elim (drops_inv_skip2 … HY) -HY #K2 #V2 #HK21 #HV12 #H destruct
-  /4 width=12 by aaa_lref_gen, fqup_lref, drops_inv_gen/
-| #l #HG #HL #HT #A #H #L2 #c #f #HL21 #X #HX -IH -c -f
+  lapply (drops_tls_at … Hf … HY) -HY #HY -Hf
+  elim (drops_inv_skip2 … HY) -HY #Z #K2 #HK21 #HZ #H destruct
+  elim (liftsb_inv_pair_sn … HZ) -HZ #V2 #HV12 #H destruct
+  /4 width=12 by aaa_lref_drops, fqup_lref, drops_inv_gen/
+| #l #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX -b -f -IH
   elim (aaa_inv_gref … H)
-| #p * #V1 #T1 #HG #HL #HT #A #H #L2 #c #f #HL21 #X #HX
+| #p * #V1 #T1 #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX
   [ elim (aaa_inv_abbr … H) -H #B #HB #HA
     elim (lifts_inv_bind1 …  HX) -HX #V2 #T2 #HV12 #HT12 #H destruct
-    /4 width=9 by aaa_abbr, drops_skip/
+    /5 width=9 by aaa_abbr, drops_skip, ext2_pair/
   | elim (aaa_inv_abst … H) -H #B #A0 #HB #HA #H0
-    elim (lifts_inv_bind1 …  HX) -HX #V2 #T2 #HV12 #HT12 #H destruct
-    /4 width=8 by aaa_abst, drops_skip/
+    elim (lifts_inv_bind1 … HX) -HX #V2 #T2 #HV12 #HT12 #H destruct
+    /5 width=8 by aaa_abst, drops_skip, ext2_pair/
   ]
-| * #V1 #T1 #HG #HL #HT #A #H #L2 #c #f #HL21 #X #HX
+| * #V1 #T1 #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX
   [ elim (aaa_inv_appl … H) -H #B #HB #HA
     elim (lifts_inv_flat1 …  HX) -HX #V2 #T2 #HV12 #HT12 #H destruct
     /3 width=10 by aaa_appl/
@@ -84,31 +86,32 @@ qed-.
 (* Inversion lemmas with generic slicing for local environments *************)
 
 (* Basic_2A1: includes: aaa_inv_lift *)
-lemma aaa_inv_lifts: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀L1,c,f. ⬇*[c, f] L2 ≡ L1 →
-                     ∀T1. ⬆*[f] T1 ≡ T2 → ⦃G, L1⦄ ⊢ T1 ⁝ A.
-@fqup_wf_ind_eq #G0 #L0 #T0 #IH #G #L2 * *
-[ #s #HG #HL #HT #A #H #L1 #c #f #HL21 #X #HX -IH -c
+lemma aaa_inv_lifts: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀b,f,L1. ⬇*[b, f] L2 ≘ L1 →
+                     ∀T1. ⬆*[f] T1 ≘ T2 → ⦃G, L1⦄ ⊢ T1 ⁝ A.
+@(fqup_wf_ind_eq (Ⓣ)) #G0 #L0 #T0 #IH #G #L2 * *
+[ #s #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX -b -IH
   lapply (aaa_inv_sort … H) -H #H destruct
   >(lifts_inv_sort2 … HX) -HX //
-| #i2 #HG #HL #HT #A #H #L1 #c #f #HL21 #X #HX
-  elim (aaa_inv_lref_gen … H) -H #J #K2 #V2 #HLK2 #HA
+| #i2 #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX
+  elim (aaa_inv_lref_drops … H) -H #J #K2 #V2 #HLK2 #HA
   elim (lifts_inv_lref2 … HX) -HX #i1 #Hf #H destruct
   lapply (drops_split_div … HL21 (𝐔❴i1❵) ???) -HL21 [4: * |*: // ] #Y #HLK1 #HY
   lapply (drops_conf … HLK2 … HY ??) -HY [1,2: /2 width=6 by after_uni_dx/ ] #HY
-  lapply (drops_inv_tls_at … Hf … HY) -HY #HY -Hf
-  elim (drops_inv_skip1 … HY) -HY #K1 #V1 #HK21 #HV12 #H destruct
-  /4 width=12 by aaa_lref_gen, fqup_lref, drops_inv_F/
-| #l #HG #HL #HT #A #H #L1 #c #f #HL21 #X #HX -IH -c -f
+  lapply (drops_tls_at … Hf … HY) -HY #HY -Hf
+  elim (drops_inv_skip1 … HY) -HY #Z #K1 #HK21 #HZ #H destruct
+  elim (liftsb_inv_pair_dx … HZ) -HZ #V1 #HV12 #H destruct
+  /4 width=12 by aaa_lref_drops, fqup_lref, drops_inv_F/
+| #l #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX -IH -b -f
   elim (aaa_inv_gref … H)
-| #p * #V2 #T2 #HG #HL #HT #A #H #L1 #c #f #HL21 #X #HX
+| #p * #V2 #T2 #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX
   [ elim (aaa_inv_abbr … H) -H #B #HB #HA
     elim (lifts_inv_bind2 …  HX) -HX #V1 #T1 #HV12 #HT12 #H destruct
-    /4 width=9 by aaa_abbr, drops_skip/
+    /5 width=9 by aaa_abbr, drops_skip, ext2_pair/
   | elim (aaa_inv_abst … H) -H #B #A0 #HB #HA #H0
     elim (lifts_inv_bind2 …  HX) -HX #V1 #T1 #HV12 #HT12 #H destruct
-    /4 width=8 by aaa_abst, drops_skip/
+    /5 width=8 by aaa_abst, drops_skip, ext2_pair/
   ]
-| * #V2 #T2 #HG #HL #HT #A #H #L1 #c #f #HL21 #X #HX
+| * #V2 #T2 #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX
   [ elim (aaa_inv_appl … H) -H #B #HB #HA
     elim (lifts_inv_flat2 …  HX) -HX #V1 #T1 #HV12 #HT12 #H destruct
     /3 width=10 by aaa_appl/