X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcnx_simple.ma;h=ad4afa831fd589172358a1ddc3802f58326672b8;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=322930c7fd6825008ea2aaf9fe1fcc4001406350;hpb=db020b4218272e2e35641ce3bc3b0a9b3afda899;p=helm.git

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 322930c7f..ad4afa831 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx_simple.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx_simple.ma
@@ -19,29 +19,29 @@ include "basic_2/rt_transition/cnx.ma".
 
 (* Inversion lemmas with simple terms ***************************************)
 
-lemma cnx_inv_appl: ∀h,G,L,V,T. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃ⓐV.T⦄ →
-                    ∧∧ ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃V⦄ & ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ & 𝐒⦃T⦄.
+lemma cnx_inv_appl: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓐV.T❫ →
+                    ∧∧ ❪G,L❫ ⊢ ⬈[h] 𝐍❪V❫ & ❪G,L❫ ⊢ ⬈[h] 𝐍❪T❫ & 𝐒❪T❫.
 #h #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 (𝐔❴1❵)) #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 (𝐔❨1❩)) #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,G,L,V,T. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃V⦄ → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ → 𝐒⦃T⦄ →
-                       ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃ⓐV.T⦄.
+lemma cnx_appl_simple: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪V❫ → ❪G,L❫ ⊢ ⬈[h] 𝐍❪T❫ → 𝐒❪T❫ →
+                       ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓐV.T❫.
 #h #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.