X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcsx_csx.ma;h=3702ba2458fda8782377de2e10c8ea358f5fce27;hb=4173283e148199871d787c53c0301891deb90713;hp=e1df7c0292b68153016dfaa2da9ef071922c3756;hpb=b11e1907f99bea1de50db890d849ba5469d2e0e7;p=helm.git

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 e1df7c029..3702ba245 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
@@ -12,36 +12,35 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/syntax/tdeq_tdeq.ma".
-include "basic_2/rt_transition/lfpx_lfdeq.ma".
-include "basic_2/rt_computation/csx.ma".
+include "basic_2/rt_transition/lpx_rdeq.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
+lemma csx_tdeq_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 (tdeq_cpx_trans … HT2 … HT21) -HT21
 /4 width=5 by tdeq_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 (tdeq_dec T1 T2) /3 width=4 by csx_tdeq_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 (tdeq_false_inv_pair … H2) -H2
+  elim (tdneq_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/
@@ -49,3 +48,35 @@ lemma csx_cast: ∀h,o,G,L,W. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃W⦄ →
 |*: /3 width=3 by csx_cpx_trans/
 ]
 qed.
+
+(* Basic_1: was just: sn3_abbr *)
+(* Basic_2A1: was: csx_lref_bind *)
+lemma csx_lref_pair: ∀h,I,G,L,K,V,i. ⬇*[i] L ≘ K.ⓑ{I}V →
+                     ⦃G, K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃#i⦄.
+#h #I #G #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
+  lapply (drops_mono … HLK0 … HLK) -HLK #H destruct
+  /3 width=8 by csx_lifts, csx_cpx_trans, drops_isuni_fwd_drop2/
+]
+qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_1: was: sn3_gen_def *)
+(* Basic_2A1: was: csx_inv_lref_bind *)
+lemma csx_inv_lref_pair: ∀h,I,G,L,K,V,i. ⬇*[i] L ≘ K.ⓑ{I}V →
+                         ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃#i⦄ → ⦃G, K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄.
+#h #I #G #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,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, ex2_3_intro, ex1_2_intro, or3_intro2, or3_intro1/
+qed-.