X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flsuba_aaa.ma;h=7bd8f30edc342c603fadae775c6a39a49adffec3;hp=f4dd5a524eb1f17e3562389f49a49cf92f4af109;hb=222044da28742b24584549ba86b1805a87def070;hpb=ff7754f834f937bfe2384c7703cf63f552885395

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_aaa.ma
index f4dd5a524..7bd8f30ed 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_aaa.ma
@@ -15,41 +15,39 @@
 include "basic_2/static/aaa_aaa.ma".
 include "basic_2/static/lsuba.ma".
 
-(* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
+(* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
 
-(* Properties concerning atomic arity assignment ****************************)
+(* Properties with atomic arity assignment **********************************)
 
 lemma lsuba_aaa_conf: ∀G,L1,V,A. ⦃G, L1⦄ ⊢ V ⁝ A →
-                      ∀L2. G ⊢ L1 ⁝⫃ L2 → ⦃G, L2⦄ ⊢ V ⁝ A.
+                      ∀L2. G ⊢ L1 ⫃⁝ L2 → ⦃G, L2⦄ ⊢ V ⁝ A.
 #G #L1 #V #A #H elim H -G -L1 -V -A
 [ //
-| #I #G #L1 #K1 #V #A #i #HLK1 #HV #IHV #L2 #HL12
-  elim (lsuba_ldrop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
-  elim (lsuba_inv_pair1 … H) -H * #K2
-  [ #HK12 #H destruct /3 width=5 by aaa_lref/
-  | #W0 #V0 #A0 #HV0 #HW0 #_ #H1 #H2 #H3 destruct
-    lapply (aaa_mono … HV0 … HV) #H destruct -V0 /2 width=5 by aaa_lref/
-  ]
-| /4 width=2 by lsuba_pair, aaa_abbr/
-| /4 width=1 by lsuba_pair, aaa_abst/
+| #I #G #L1 #V #A #HA #IH #L2 #H
+  elim (lsuba_inv_bind1 … H) -H * /3 width=1 by aaa_zero/
+  #L0 #W0 #V0 #A0 #HV0 #HW0 #HL10 #H1 #H2 destruct
+  lapply (aaa_mono … HV0 … HA) #H destruct -V0 -L1 /2 width=1 by aaa_zero/
+| #I #G #K1 #A #i #_ #IH #L2 #H
+  elim (lsuba_inv_bind1 … H) -H * /3 width=1 by aaa_lref/
+| /4 width=2 by lsuba_bind, aaa_abbr/
+| /4 width=1 by lsuba_bind, aaa_abst/
 | /3 width=3 by aaa_appl/
 | /3 width=1 by aaa_cast/
 ]
 qed-.
 
 lemma lsuba_aaa_trans: ∀G,L2,V,A. ⦃G, L2⦄ ⊢ V ⁝ A →
-                       ∀L1. G ⊢ L1 ⁝⫃ L2 → ⦃G, L1⦄ ⊢ V ⁝ A.
+                       ∀L1. G ⊢ L1 ⫃⁝ L2 → ⦃G, L1⦄ ⊢ V ⁝ A.
 #G #L2 #V #A #H elim H -G -L2 -V -A
 [ //
-| #I #G #L2 #K2 #V #A #i #HLK2 #H1V #IHV #L1 #HL12
-  elim (lsuba_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
-  elim (lsuba_inv_pair2 … H) -H * #K1
-  [ #HK12 #H destruct /3 width=5 by aaa_lref/
-  | #V0 #A0 #HV0 #H2V #_ #H1 #H2 destruct
-    lapply (aaa_mono … H2V … H1V) #H destruct -K2 /2 width=5 by aaa_lref/
-  ]
-| /4 width=2 by lsuba_pair, aaa_abbr/
-| /4 width=1 by lsuba_pair, aaa_abst/
+| #I #G #L2 #V #A #HA #IH #L1 #H
+  elim (lsuba_inv_bind2 … H) -H * /3 width=1 by aaa_zero/
+  #L0 #V0 #W0 #A0 #HV0 #HW0 #HL02 #H1 #H2 destruct
+  lapply (aaa_mono … HW0 … HA) #H destruct -L2 /2 width=1 by aaa_zero/
+| #I #G #K2 #A #i #_ #IH #L1 #H
+  elim (lsuba_inv_bind2 … H) -H * /3 width=1 by aaa_lref/
+| /4 width=2 by lsuba_bind, aaa_abbr/
+| /4 width=1 by lsuba_bind, aaa_abst/
 | /3 width=3 by aaa_appl/
 | /3 width=1 by aaa_cast/
 ]