update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / csx_lsubr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma
index 5e32b0e6d3e007132aefaadd069a729c5b39eb03..5b180f3da91a1f73b0d6154d41cc8a895cd00572 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma
@@ -20,8 +20,8 @@ include "basic_2/rt_computation/csx_csx.ma".
 (* Advanced properties ******************************************************)
 
 fact csx_appl_beta_aux (h) (G):
-     â\88\80p,L,U1. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83U1â¦\84 →
-     ∀V,W,T1. U1 = ⓓ{p}ⓝW.V.T1 → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.ⓛ{p}W.T1⦄.
+     â\88\80p,L,U1. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªU1â\9d« →
+     ∀V,W,T1. U1 = ⓓ[p]ⓝW.V.T1 → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⓐV.ⓛ[p]W.T1❫.
 #h #G #p #L #X #H @(csx_ind … H) -X
 #X #HT1 #IHT1 #V #W #T1 #H1 destruct
 @csx_intro #X #H1 #H2
@@ -31,9 +31,9 @@ elim (cpx_inv_appl1 … H1) -H1 *
   @IHT1 -IHT1 [4: // | skip ]
   [ lapply (lsubr_cpx_trans … HLT0 (L.ⓓⓝW.V) ?) -HLT0 -H2
     /3 width=1 by cpx_bind, cpx_flat, lsubr_beta/
-  | #H elim (tdeq_inv_pair … H) -H
-    #_ #H elim (tdeq_inv_pair … H) -H
-    #_ /4 width=1 by tdeq_pair/
+  | #H elim (teqx_inv_pair … H) -H
+    #_ #H elim (teqx_inv_pair … H) -H
+    #_ /4 width=1 by teqx_pair/
   ]
 | -IHT1 -H2 #q #V0 #W0 #W2 #T0 #T2 #HLV0 #HLW02 #HLT02 #H1 #H3 destruct
   lapply (lsubr_cpx_trans … HLT02 (L.ⓓⓝW0.V) ?) -HLT02
@@ -44,34 +44,34 @@ qed-.
 
 (* Basic_1: was just: sn3_beta *)
 lemma csx_appl_beta (h) (G):
-      â\88\80p,L,V,W,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\93{p}â\93\9dW.V.Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\90V.â\93\9b{p}W.Tâ¦\84.
+      â\88\80p,L,V,W,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\93\93[p]â\93\9dW.V.Tâ\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\93\90V.â\93\9b[p]W.Tâ\9d«.
 /2 width=3 by csx_appl_beta_aux/ qed.
 
 (* Advanced forward lemmas **************************************************)
 
 fact csx_fwd_bind_dx_unit_aux (h) (G):
-     â\88\80L,U. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Uâ¦\84 →
-     ∀p,I,J,V,T. U = ⓑ{p,I}V.T → ⦃G,L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+     â\88\80L,U. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªUâ\9d« →
+     ∀p,I,J,V,T. U = ⓑ[p,I]V.T → ❪G,L.ⓤ[J]❫ ⊢ ⬈*[h] 𝐒❪T❫.
 #h #G #L #U #H elim H -H #U0 #_ #IH #p #I #J #V #T #H destruct
 @csx_intro #T2 #HLT2 #HT2
-@(IH (ⓑ{p, I}V.T2)) -IH /2 width=4 by cpx_bind_unit/ -HLT2
-#H elim (tdeq_inv_pair … H) -H /2 width=1 by/
+@(IH (ⓑ[p, I]V.T2)) -IH /2 width=4 by cpx_bind_unit/ -HLT2
+#H elim (teqx_inv_pair … H) -H /2 width=1 by/
 qed-.
 
 lemma csx_fwd_bind_dx_unit (h) (G):
-      â\88\80p,I,L,V,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\91{p,I}V.Tâ¦\84 →
-      â\88\80J. â¦\83G,L.â\93¤{J}â¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84.
+      â\88\80p,I,L,V,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\93\91[p,I]V.Tâ\9d« →
+      â\88\80J. â\9dªG,L.â\93¤[J]â\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d«.
 /2 width=6 by csx_fwd_bind_dx_unit_aux/ qed-.
 
 lemma csx_fwd_bind_unit (h) (G):
-      â\88\80p,I,L,V,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\91{p,I}V.Tâ¦\84 →
-      â\88\80J. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Vâ¦\84 â\88§ â¦\83G,L.â\93¤{J}â¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84.
+      â\88\80p,I,L,V,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\93\91[p,I]V.Tâ\9d« →
+      â\88\80J. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªVâ\9d« â\88§ â\9dªG,L.â\93¤[J]â\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d«.
 /3 width=4 by csx_fwd_pair_sn, csx_fwd_bind_dx_unit, conj/ qed-.
 
 (* Properties with restricted refinement for local environments *************)
 
 lemma csx_lsubr_conf (h) (G):
-      â\88\80L1,T. â¦\83G,L1â¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â\88\80L2. L1 â«\83 L2 â\86\92 â¦\83G,L2â¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84.
+      â\88\80L1,T. â\9dªG,L1â\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\88\80L2. L1 â«\83 L2 â\86\92 â\9dªG,L2â\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d«.
 #h #G #L1 #T #H
 @(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
 @csx_intro #T2 #HT12 #HnT12