partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / aaa_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/aaa_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/aaa_drops.ma
index b006c2d21cf1a076f10a966618d10f008053e411..b501bd3a6ae785c70b309eac5d4a30068805ed08 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/aaa_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/aaa_drops.ma
@@ -22,11 +22,11 @@ include "static_2/static/aaa.ma".
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: was: aaa_lref *)
-lemma aaa_lref_drops: â\88\80I,G,K,V,B,i,L. â¬\87*[i] L â\89\98 K.â\93\91{I}V â\86\92 â¦\83G,Kâ¦\84 â\8a¢ V â\81\9d B â\86\92 â¦\83G,Lâ¦\84 ⊢ #i ⁝ B.
+lemma aaa_lref_drops: â\88\80I,G,K,V,B,i,L. â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9dªG,Kâ\9d« â\8a¢ V â\81\9d B â\86\92 â\9dªG,Lâ\9d« ⊢ #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_bind2_isuni_next … H) -H // *
+| #i #IH #L <pr_uni_succ #H #HB lapply (drops_inv_bind2_isuni_next … H) -H // *
   #Z #Y #HY #H destruct /3 width=1 by aaa_lref/
 ]
 qed.
@@ -34,8 +34,8 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_2A1: was: aaa_inv_lref *)
-lemma aaa_inv_lref_drops: â\88\80G,A,i,L. â¦\83G,Lâ¦\84 ⊢ #i ⁝ A →
-                          â\88\83â\88\83I,K,V. â¬\87*[i] L â\89\98 K.â\93\91{I}V & â¦\83G,Kâ¦\84 ⊢ V ⁝ A.
+lemma aaa_inv_lref_drops: â\88\80G,A,i,L. â\9dªG,Lâ\9d« ⊢ #i ⁝ A →
+                          â\88\83â\88\83I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V & â\9dªG,Kâ\9d« ⊢ 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
@@ -43,12 +43,19 @@ lemma aaa_inv_lref_drops: ∀G,A,i,L. ⦃G,L⦄ ⊢ #i ⁝ A →
 ]
 qed-.
 
+lemma aaa_pair_inv_lref (G) (L) (i):
+      ∀A. ❪G,L❫ ⊢ #i ⁝ A → ∀I,K,V. ⇩[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⁝ A.
+#G #L #i #A #H #I #K #V #HLK
+elim (aaa_inv_lref_drops … H) -H #J #Y #X #HLY #HX
+lapply (drops_mono … HLY … HLK) -L -i #H destruct //
+qed-.
+
 (* Properties with generic slicing for local environments *******************)
 
 (* Basic_2A1: includes: aaa_lift *)
 (* Note: it should use drops_split_trans_pair2 *)
-lemma aaa_lifts: â\88\80G,L1,T1,A. â¦\83G,L1â¦\84 â\8a¢ T1 â\81\9d A â\86\92 â\88\80b,f,L2. â¬\87*[b,f] L2 ≘ L1 →
-                 â\88\80T2. â¬\86*[f] T1 â\89\98 T2 â\86\92 â¦\83G,L2â¦\84 ⊢ T2 ⁝ A.
+lemma aaa_lifts: â\88\80G,L1,T1,A. â\9dªG,L1â\9d« â\8a¢ T1 â\81\9d A â\86\92 â\88\80b,f,L2. â\87©*[b,f] L2 ≘ L1 →
+                 â\88\80T2. â\87§*[f] T1 â\89\98 T2 â\86\92 â\9dªG,L2â\9d« ⊢ 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
@@ -57,7 +64,7 @@ lemma aaa_lifts: ∀G,L1,T1,A. ⦃G,L1⦄ ⊢ T1 ⁝ A → ∀b,f,L2. ⬇*[b,f]
   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
+  elim (drops_split_trans … H) -H [ |*: /2 width=6 by pr_after_nat_uni/ ] #Y #HLK2 #HY
   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
@@ -86,8 +93,8 @@ qed-.
 (* Inversion lemmas with generic slicing for local environments *************)
 
 (* Basic_2A1: includes: aaa_inv_lift *)
-lemma aaa_inv_lifts: â\88\80G,L2,T2,A. â¦\83G,L2â¦\84 â\8a¢ T2 â\81\9d A â\86\92 â\88\80b,f,L1. â¬\87*[b,f] L2 ≘ L1 →
-                     â\88\80T1. â¬\86*[f] T1 â\89\98 T2 â\86\92 â¦\83G,L1â¦\84 ⊢ T1 ⁝ A.
+lemma aaa_inv_lifts: â\88\80G,L2,T2,A. â\9dªG,L2â\9d« â\8a¢ T2 â\81\9d A â\86\92 â\88\80b,f,L1. â\87©*[b,f] L2 ≘ L1 →
+                     â\88\80T1. â\87§*[f] T1 â\89\98 T2 â\86\92 â\9dªG,L1â\9d« ⊢ 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
@@ -95,8 +102,8 @@ lemma aaa_inv_lifts: ∀G,L2,T2,A. ⦃G,L2⦄ ⊢ T2 ⁝ A → ∀b,f,L1. ⬇*[b
 | #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 â\80¦ HL21 (ð\9d\90\94â\9d´i1â\9dµ) ???) -HL21 [4: * |*: // ] #Y #HLK1 #HY
-  lapply (drops_conf … HLK2 … HY ??) -HY [1,2: /2 width=6 by after_uni_dx/ ] #HY
+  lapply (drops_split_div â\80¦ HL21 (ð\9d\90\94â\9d¨i1â\9d©) ???) -HL21 [4: * |*: // ] #Y #HLK1 #HY
+  lapply (drops_conf … HLK2 … HY ??) -HY [1,2: /2 width=6 by pr_after_nat_uni/ ] #HY
   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