milestone update in basic_2, update in ground and static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cnx_simple.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx_simple.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx_simple.ma
index 640e24d372274b829e76517cde123c6e7f8a3f32..261a220aa54b341f2cf86f85274efb7115b28072 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx_simple.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx_simple.ma
@@ -15,33 +15,34 @@
 include "basic_2/rt_transition/cpx_simple.ma".
 include "basic_2/rt_transition/cnx.ma".
 
-(* NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ********)
+(* NORMAL TERMS FOR EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION *******)
 
 (* Inversion lemmas with simple terms ***************************************)
 
-lemma cnx_inv_appl: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃ⓐV.T⦄ →
-                    ∧∧ ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃V⦄ & ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄ & 𝐒⦃T⦄.
-#h #o #G #L #V1 #T1 #HVT1 @and3_intro
+lemma cnx_inv_appl (G) (L):
+      ∀V,T. ❪G,L❫ ⊢ ⬈𝐍 ⓐV.T →
+      ∧∧ ❪G,L❫ ⊢ ⬈𝐍 V & ❪G,L❫ ⊢ ⬈𝐍 T & 𝐒❪T❫.
+#G #L #V1 #T1 #HVT1 @and3_intro
 [ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1 by cpx_pair_sn/ -HV2
-  #H elim (tdeq_inv_pair … H) -H //
+  #H elim (teqx_inv_pair … H) -H //
 | #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpx_flat/ -HT2
-  #H elim (tdeq_inv_pair … H) -H //
+  #H elim (teqx_inv_pair … H) -H //
 | generalize in match HVT1; -HVT1 elim T1 -T1 * //
   #p * #W1 #U1 #_ #_ #H
-  [ elim (lifts_total V1 (ð\9d\90\94â\9d´1â\9dµ)) #V2 #HV12
-    lapply (H (ⓓ{p}W1.ⓐV2.U1) ?) -H /2 width=3 by cpx_theta/ -HV12
-    #H elim (tdeq_inv_pair … H) -H #H destruct
-  | lapply (H (ⓓ{p}ⓝW1.V1.U1) ?) -H /2 width=1 by cpx_beta/
-    #H elim (tdeq_inv_pair … H) -H #H destruct
+  [ elim (lifts_total V1 (ð\9d\90\94â\9d¨1â\9d©)) #V2 #HV12
+    lapply (H (ⓓ[p]W1.ⓐV2.U1) ?) -H /2 width=3 by cpx_theta/ -HV12
+    #H elim (teqx_inv_pair … H) -H #H destruct
+  | lapply (H (ⓓ[p]ⓝW1.V1.U1) ?) -H /2 width=1 by cpx_beta/
+    #H elim (teqx_inv_pair … H) -H #H destruct
   ]
 ]
 qed-.
 
 (* Properties with simple terms *********************************************)
 
-lemma cnx_appl_simple: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃V⦄ → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄ → 𝐒⦃T⦄ →
-                       ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃ⓐV.T⦄.
-#h #o #G #L #V #T #HV #HT #HS #X #H elim (cpx_inv_appl1_simple … H) -H //
+lemma cnx_appl_simple (G) (L):
+      ∀V,T. ❪G,L❫ ⊢ ⬈𝐍 V → ❪G,L❫ ⊢ ⬈𝐍 T → 𝐒❪T❫ → ❪G,L❫ ⊢ ⬈𝐍 ⓐV.T.
+#G #L #V #T #HV #HT #HS #X #H elim (cpx_inv_appl1_simple … H) -H //
 #V0 #T0 #HV0 #HT0 #H destruct
-@tdeq_pair [ @HV | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
+@teqx_pair [ @HV | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
 qed.