X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcsx_lsubr.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcsx_lsubr.ma;h=5e32b0e6d3e007132aefaadd069a729c5b39eb03;hb=f76594123e375bd7852c9421fe260a7bec693a92;hp=07226df19ba10a8973595b45f7921908b426910d;hpb=a454837a256907d2f83d42ced7be847e10361ea9;p=helm.git

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 07226df19..5e32b0e6d 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma
@@ -19,9 +19,10 @@ include "basic_2/rt_computation/csx_csx.ma".
 
 (* Advanced properties ******************************************************)
 
-fact csx_appl_beta_aux: ∀h,p,G,L,U1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U1⦄ →
-                        ∀V,W,T1. U1 = ⓓ{p}ⓝW.V.T1 → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.ⓛ{p}W.T1⦄.
-#h #p #G #L #X #H @(csx_ind … H) -X
+fact csx_appl_beta_aux (h) (G):
+     ∀p,L,U1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U1⦄ →
+     ∀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
 elim (cpx_inv_appl1 … H1) -H1 *
@@ -42,23 +43,37 @@ elim (cpx_inv_appl1 … H1) -H1 *
 qed-.
 
 (* Basic_1: was just: sn3_beta *)
-lemma csx_appl_beta: ∀h,p,G,L,V,W,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}ⓝW.V.T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.ⓛ{p}W.T⦄.
+lemma csx_appl_beta (h) (G):
+      ∀p,L,V,W,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}ⓝW.V.T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.ⓛ{p}W.T⦄.
 /2 width=3 by csx_appl_beta_aux/ qed.
 
 (* Advanced forward lemmas **************************************************)
 
-fact csx_fwd_bind_dx_unit_aux: ∀h,G,L,U. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
-                               ∀p,I,J,V,T. U = ⓑ{p,I}V.T → ⦃G,L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+fact csx_fwd_bind_dx_unit_aux (h) (G):
+     ∀L,U. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
+     ∀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/
 qed-.
 
-lemma csx_fwd_bind_dx_unit: ∀h,p,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
-                            ∀J. ⦃G,L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+lemma csx_fwd_bind_dx_unit (h) (G):
+      ∀p,I,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
+      ∀J. ⦃G,L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
 /2 width=6 by csx_fwd_bind_dx_unit_aux/ qed-.
 
-lemma csx_fwd_bind_unit: ∀h,p,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
-                         ∀J. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ ∧ ⦃G,L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+lemma csx_fwd_bind_unit (h) (G):
+      ∀p,I,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
+      ∀J. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ ∧ ⦃G,L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
 /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):
+      ∀L1,T. ⦃G,L1⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ∀L2. L1 ⫃ L2 → ⦃G,L2⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+#h #G #L1 #T #H
+@(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
+@csx_intro #T2 #HT12 #HnT12
+/3 width=3 by lsubr_cpx_trans/
+qed-.