X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Frsx_csx.ma;h=f9f97bca8c91aea82c7c9dbb64d56b4e7bc738e6;hp=8e7c7793a2dacdf8c2e99fe16331415642af8564;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_csx.ma
index 8e7c7793a..f9f97bca8 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_csx.ma
@@ -21,8 +21,8 @@ include "basic_2/rt_computation/jsx_rsx.ma".
 (* Forward lemmas with strongly rt-normalizing terms ************************)
 
 fact rsx_fwd_lref_pair_csx_aux (h) (G):
-     ∀L. G ⊢ ⬈*[h,#0] 𝐒⦃L⦄ →
-     ∀I,K,V. L = K.ⓑ{I}V → ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄.
+     ∀L. G ⊢ ⬈*[h,#0] 𝐒❪L❫ →
+     ∀I,K,V. L = K.ⓑ[I]V → ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫.
 #h #G #L #H
 @(rsx_ind … H) -L #L #_ #IH #I #K #V1 #H destruct
 @csx_intro #V2 #HV12 #HnV12
@@ -34,17 +34,17 @@ fact rsx_fwd_lref_pair_csx_aux (h) (G):
 qed-.
 
 lemma rsx_fwd_lref_pair_csx (h) (G):
-      ∀I,K,V. G ⊢ ⬈*[h,#0] 𝐒⦃K.ⓑ{I}V⦄ → ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄.
+      ∀I,K,V. G ⊢ ⬈*[h,#0] 𝐒❪K.ⓑ[I]V❫ → ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫.
 /2 width=4 by rsx_fwd_lref_pair_csx_aux/ qed-.
 
 lemma rsx_fwd_lref_pair_csx_drops (h) (G):
-      ∀I,K,V,i,L. ⇩*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h,#i] 𝐒⦃L⦄ → ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄.
+      ∀I,K,V,i,L. ⇩*[i] L ≘ K.ⓑ[I]V → G ⊢ ⬈*[h,#i] 𝐒❪L❫ → ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫.
 #h #G #I #K #V #i elim i -i
 [ #L #H >(drops_fwd_isid … H) -H
   /2 width=2 by rsx_fwd_lref_pair_csx/
 | #i #IH #L #H1 #H2
   elim (drops_inv_bind2_isuni_next … H1) -H1 // #J #Y #HY #H destruct
-  lapply (rsx_inv_lifts … H2 … (𝐔❴1❵) ?????) -H2
+  lapply (rsx_inv_lifts … H2 … (𝐔❨1❩) ?????) -H2
   /3 width=6 by drops_refl, drops_drop/
 ]
 qed-.
@@ -52,20 +52,20 @@ qed-.
 (* Inversion lemmas with strongly rt-normalizing terms **********************)
 
 lemma rsx_inv_lref_pair (h) (G):
-      ∀I,K,V. G ⊢ ⬈*[h,#0] 𝐒⦃K.ⓑ{I}V⦄ →
-      ∧∧ ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄  & G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
+      ∀I,K,V. G ⊢ ⬈*[h,#0] 𝐒❪K.ⓑ[I]V❫ →
+      ∧∧ ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫  & G ⊢ ⬈*[h,V] 𝐒❪K❫.
 /3 width=2 by rsx_fwd_lref_pair_csx, rsx_fwd_pair, conj/ qed-.
 
 lemma rsx_inv_lref_pair_drops (h) (G):
-      ∀I,K,V,i,L. ⇩*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h,#i] 𝐒⦃L⦄ →
-      ∧∧ ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ & G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
+      ∀I,K,V,i,L. ⇩*[i] L ≘ K.ⓑ[I]V → G ⊢ ⬈*[h,#i] 𝐒❪L❫ →
+      ∧∧ ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫ & G ⊢ ⬈*[h,V] 𝐒❪K❫.
 /3 width=5 by rsx_fwd_lref_pair_csx_drops, rsx_fwd_lref_pair_drops, conj/ qed-.
 
 lemma rsx_inv_lref_drops (h) (G):
-      ∀L,i. G ⊢ ⬈*[h,#i] 𝐒⦃L⦄ →
-      ∨∨ ⇩*[Ⓕ,𝐔❴i❵] L ≘ ⋆
-       | ∃∃I,K. ⇩*[i] L ≘ K.ⓤ{I}
-       | ∃∃I,K,V. ⇩*[i] L ≘ K.ⓑ{I}V & ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ & G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
+      ∀L,i. G ⊢ ⬈*[h,#i] 𝐒❪L❫ →
+      ∨∨ ⇩*[Ⓕ,𝐔❨i❩] L ≘ ⋆
+       | ∃∃I,K. ⇩*[i] L ≘ K.ⓤ[I]
+       | ∃∃I,K,V. ⇩*[i] L ≘ K.ⓑ[I]V & ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫ & G ⊢ ⬈*[h,V] 𝐒❪K❫.
 #h #G #L #i #H elim (drops_F_uni L i)
 [ /2 width=1 by or3_intro0/
 | * * /4 width=10 by rsx_fwd_lref_pair_csx_drops, rsx_fwd_lref_pair_drops, ex3_3_intro, ex1_2_intro, or3_intro2, or3_intro1/
@@ -77,9 +77,9 @@ qed-.
 (* Note: swapping the eliminations to avoid rsx_cpx_trans: no solution found *)
 (* Basic_2A1: uses: lsx_lref_be_lpxs *)
 lemma rsx_lref_pair_lpxs (h) (G):
-      ∀K1,V. ⦃G,K1⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ →
-      ∀K2. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ → ⦃G,K1⦄ ⊢ ⬈*[h] K2 →
-      ∀I. G ⊢ ⬈*[h,#0] 𝐒⦃K2.ⓑ{I}V⦄.
+      ∀K1,V. ❪G,K1❫ ⊢ ⬈*[h] 𝐒❪V❫ →
+      ∀K2. G ⊢ ⬈*[h,V] 𝐒❪K2❫ → ❪G,K1❫ ⊢ ⬈*[h] K2 →
+      ∀I. G ⊢ ⬈*[h,#0] 𝐒❪K2.ⓑ[I]V❫.
 #h #G #K1 #V #H
 @(csx_ind_cpxs … H) -V #V0 #_ #IHV0 #K2 #H
 @(rsx_ind … H) -K2 #K0 #HK0 #IHK0 #HK10 #I
@@ -96,25 +96,25 @@ elim (teqx_dec V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
 qed.
 
 lemma rsx_lref_pair (h) (G):
-      ∀K,V. ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → G ⊢ ⬈*[h,V] 𝐒⦃K⦄ → ∀I. G ⊢ ⬈*[h,#0] 𝐒⦃K.ⓑ{I}V⦄.
+      ∀K,V. ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫ → G ⊢ ⬈*[h,V] 𝐒❪K❫ → ∀I. G ⊢ ⬈*[h,#0] 𝐒❪K.ⓑ[I]V❫.
 /2 width=3 by rsx_lref_pair_lpxs/ qed.
 
 (* Basic_2A1: uses: lsx_lref_be *)
 lemma rsx_lref_pair_drops (h) (G):
-      ∀K,V. ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → G ⊢ ⬈*[h,V] 𝐒⦃K⦄ →
-      ∀I,i,L. ⇩*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h,#i] 𝐒⦃L⦄.
+      ∀K,V. ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫ → G ⊢ ⬈*[h,V] 𝐒❪K❫ →
+      ∀I,i,L. ⇩*[i] L ≘ K.ⓑ[I]V → G ⊢ ⬈*[h,#i] 𝐒❪L❫.
 #h #G #K #V #HV #HK #I #i elim i -i
 [ #L #H >(drops_fwd_isid … H) -H /2 width=1 by rsx_lref_pair/
 | #i #IH #L #H
   elim (drops_inv_bind2_isuni_next … H) -H // #J #Y #HY #H destruct
-  @(rsx_lifts … (𝐔❴1❵)) /3 width=6 by drops_refl, drops_drop/ (**) (* full auto fails *)
+  @(rsx_lifts … (𝐔❨1❩)) /3 width=6 by drops_refl, drops_drop/ (**) (* full auto fails *)
 ]
 qed.
 
 (* Main properties with strongly rt-normalizing terms ***********************)
 
 (* Basic_2A1: uses: csx_lsx *)
-theorem csx_rsx (h) (G): ∀L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → G ⊢ ⬈*[h,T] 𝐒⦃L⦄.
+theorem csx_rsx (h) (G): ∀L,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → G ⊢ ⬈*[h,T] 𝐒❪L❫.
 #h #G #L #T @(fqup_wf_ind_eq (Ⓣ) … G L T) -G -L -T
 #Z #Y #X #IH #G #L * *
 [ //