update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
index badaae1ca9d9315d3385d75a0ec35fe1c3fd6d1a..0500e42547b2dc03494919ce9cfc8ef146f60ce4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
@@ -12,35 +12,38 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_transition/lfpx_lfdeq.ma".
+include "basic_2/rt_transition/lpx_reqx.ma".
 include "basic_2/rt_computation/csx_drops.ma".
 
-(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
 
 (* Advanced properties ******************************************************)
 
-lemma csx_tdeq_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                      ∀T2. T1 ≛[h, o] T2 → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
-#h #o #G #L #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
-@csx_intro #T1 #HT21 #HnT21 elim (tdeq_cpx_trans … HT2 … HT21) -HT21
-/4 width=5 by tdeq_repl/
+lemma csx_teqx_trans (h) (G):
+      ∀L,T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ →
+      ∀T2. T1 ≛ T2 → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T2❫.
+#h #G #L #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
+@csx_intro #T1 #HT21 #HnT21 elim (teqx_cpx_trans … HT2 … HT21) -HT21
+/4 width=5 by teqx_repl/
 qed-.
 
-lemma csx_cpx_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                     ∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
-#h #o #G #L #T1 #H @(csx_ind … H) -T1 #T1 #HT1 #IHT1 #T2 #HLT12
-elim (tdeq_dec h o T1 T2) /3 width=4 by csx_tdeq_trans/
+lemma csx_cpx_trans (h) (G):
+      ∀L,T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ →
+      ∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T2❫.
+#h #G #L #T1 #H @(csx_ind … H) -T1 #T1 #HT1 #IHT1 #T2 #HLT12
+elim (teqx_dec T1 T2) /3 width=4 by csx_teqx_trans/
 qed-.
 
 (* Basic_1: was just: sn3_cast *)
-lemma csx_cast: ∀h,o,G,L,W. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃W⦄ →
-                ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓝW.T⦄.
-#h #o #G #L #W #HW @(csx_ind … HW) -W
+lemma csx_cast (h) (G):
+      ∀L,W. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪W❫ →
+      ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⓝW.T❫.
+#h #G #L #W #HW @(csx_ind … HW) -W
 #W #HW #IHW #T #HT @(csx_ind … HT) -T
 #T #HT #IHT @csx_intro
 #X #H1 #H2 elim (cpx_inv_cast1 … H1) -H1
 [ * #W0 #T0 #HLW0 #HLT0 #H destruct
-  elim (tdneq_inv_pair … H2) -H2
+  elim (tneqx_inv_pair … H2) -H2
   [ -W -T #H elim H -H //
   | -HW -IHT /3 width=3 by csx_cpx_trans/
   | -HW -HT -IHW /4 width=3 by csx_cpx_trans, cpx_pair_sn/
@@ -51,9 +54,10 @@ qed.
 
 (* Basic_1: was just: sn3_abbr *)
 (* Basic_2A1: was: csx_lref_bind *)
-lemma csx_lref_pair: ∀h,o,I,G,L,K,V,i. ⬇*[i] L ≡ K.ⓑ{I}V →
-                     ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃#i⦄.
-#h #o #I #G #L #K #V #i #HLK #HV
+lemma csx_lref_pair_drops (h) (G):
+      ∀I,L,K,V,i. ⇩*[i] L ≘ K.ⓑ[I]V →
+      ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪#i❫.
+#h #G #I #L #K #V #i #HLK #HV
 @csx_intro #X #H #Hi elim (cpx_inv_lref1_drops … H) -H
 [ #H destruct elim Hi //
 | -Hi * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HV1
@@ -66,17 +70,19 @@ qed.
 
 (* Basic_1: was: sn3_gen_def *)
 (* Basic_2A1: was: csx_inv_lref_bind *)
-lemma csx_inv_lref_pair: ∀h,o,I,G,L,K,V,i. ⬇*[i] L ≡ K.ⓑ{I}V →
-                         ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃#i⦄ → ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄.
-#h #o #I #G #L #K #V #i #HLK #Hi
-elim (lifts_total V (𝐔❴⫯i❵))
+lemma csx_inv_lref_pair_drops (h) (G):
+      ∀I,L,K,V,i. ⇩*[i] L ≘ K.ⓑ[I]V →
+      ❪G,L❫ ⊢ ⬈*[h] 𝐒❪#i❫ → ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫.
+#h #G #I #L #K #V #i #HLK #Hi
+elim (lifts_total V (𝐔❨↑i❩))
 /4 width=9 by csx_inv_lifts, csx_cpx_trans, cpx_delta_drops, drops_isuni_fwd_drop2/
 qed-.
 
-lemma csx_inv_lref: ∀h,o,G,L,i. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃#i⦄ →
-                    ∨∨ ⬇*[Ⓕ, 𝐔❴i❵] L ≡ ⋆
-                     | ∃∃I,K. ⬇*[i] L ≡ K.ⓤ{I}
-                     | ∃∃I,K,V. ⬇*[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄.
-#h #o #G #L #i #H elim (drops_F_uni L i) /2 width=1 by or3_intro0/
-* * /4 width=9 by csx_inv_lref_pair, ex2_3_intro, ex1_2_intro, or3_intro2, or3_intro1/
+lemma csx_inv_lref_drops (h) (G):
+      ∀L,i. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪#i❫ →
+      ∨∨ ⇩*[Ⓕ,𝐔❨i❩] L ≘ ⋆
+       | ∃∃I,K. ⇩*[i] L ≘ K.ⓤ[I]
+       | ∃∃I,K,V. ⇩*[i] L ≘ K.ⓑ[I]V & ❪G,K❫ ⊢ ⬈*[h] 𝐒❪V❫.
+#h #G #L #i #H elim (drops_F_uni L i) /2 width=1 by or3_intro0/
+* * /4 width=9 by csx_inv_lref_pair_drops, ex2_3_intro, ex1_2_intro, or3_intro2, or3_intro1/
 qed-.