update in basic_2 and apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_simple.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_simple.ma
index 20039dafebbca566559ecca2fe3ffd8a65d8fbe5..bd1e11c003bccb3175c6d0f082dc3d988d42867c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_simple.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr_simple.ma
@@ -20,14 +20,15 @@ include "basic_2/rt_transition/cnr.ma".
 (* Inversion lemmas with simple terms ***************************************)
 
 lemma cnr_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⦄.
+      ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] ⓐV.T →
+      ∧∧ ❪G,L❫ ⊢ ➡𝐍[h,0] V & ❪G,L❫ ⊢ ➡𝐍[h,0] T & 𝐒❪T❫.
 #h #G #L #V1 #T1 #HVT1 @and3_intro
 [ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1 by cpr_pair_sn/ -HV2 #H destruct //
 | #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpr_flat/ -HT2 #H destruct //
 | generalize in match HVT1; -HVT1 elim T1 -T1 * // #a * #W1 #U1 #_ #_ #H
-  [ elim (lifts_total V1 ð\9d\90\94â\9d´1â\9dµ) #V2 #HV12
-    lapply (H (ⓓ{a}W1.ⓐV2.U1) ?) -H /2 width=3 by cpm_theta/ -HV12 #H destruct
-  | lapply (H (ⓓ{a}ⓝW1.V1.U1) ?) -H /2 width=1 by cpm_beta/ #H destruct
+  [ elim (lifts_total V1 ð\9d\90\94â\9d¨1â\9d©) #V2 #HV12
+    lapply (H (ⓓ[a]W1.ⓐV2.U1) ?) -H /2 width=3 by cpm_theta/ -HV12 #H destruct
+  | lapply (H (ⓓ[a]ⓝW1.V1.U1) ?) -H /2 width=1 by cpm_beta/ #H destruct
   ]
 ]
 qed-.
@@ -36,7 +37,7 @@ qed-.
 
 (* Basic_1: was only: nf2_appl_lref *)
 lemma cnr_appl_simple (h) (G) (L):
-      â\88\80V,T. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83Vâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83Tâ¦\84 â\86\92 ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83â\93\90V.Tâ¦\84.
+      â\88\80V,T. â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] V â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] T â\86\92 ð\9d\90\92â\9dªTâ\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] â\93\90V.T.
 #h #G #L #V #T #HV #HT #HS #X #H
 elim (cpm_inv_appl1_simple … H) -H // #V0 #T0 #HV0 #HT0 #H destruct
 <(HV … HV0) -V0 <(HT … HT0) -T0 //