some resuls on pointwise extensions (all of them are now in the

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpxs_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
index 2d67976674c49b0249f1202604492f463fe81cd8..92b694f91ea311075d06391d7f97f32b4a1a17a9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
@@ -14,7 +14,7 @@
 
 include "basic_2/substitution/fqus_fqus.ma".
 include "basic_2/unfold/lsstas_lift.ma".
-include "basic_2/reduction/cpx_lift.ma".
+include "basic_2/reduction/llpx_ldrop.ma".
 include "basic_2/computation/cpxs.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
@@ -33,21 +33,24 @@ lapply (lsstas_da_conf … HT1 … Hl2) -HT1
 qed.
 
 lemma cpxs_delta: ∀h,g,I,G,L,K,V,V2,i.
-                  ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ➡*[h, g] V2 →
-                  ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡*[h, g] W2.
+                  ⇩[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ➡*[h, g] V2 →
+                  ∀W2. ⇧[0, i+1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡*[h, g] W2.
 #h #g #I #G #L #K #V #V2 #i #HLK #H elim H -V2
 [ /3 width=9 by cpx_cpxs, cpx_delta/
 | #V1 lapply (ldrop_fwd_drop2 … HLK) -HLK
-  elim (lift_total V1 0 (i+1)) /4 width=11 by cpx_lift, cpxs_strap1/
+  elim (lift_total V1 0 (i+1)) /4 width=12 by cpx_lift, cpxs_strap1/
 ]
 qed.
 
+lemma cpxs_llpx_conf: ∀h,g,G. s_r_confluent1 … (cpxs h g G) (llpx h g G 0).
+/3 width=5 by llpx_cpx_conf, s_r_conf1_LTC1/ qed-.
+
 (* Advanced inversion lemmas ************************************************)
 
 lemma cpxs_inv_lref1: ∀h,g,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡*[h, g] T2 →
                       T2 = #i ∨
-                      ∃∃I,K,V1,T1. ⇩[0, i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ➡*[h, g] T1 &
-                                   ⇧[0, i + 1] T1 ≡ T2.
+                      ∃∃I,K,V1,T1. ⇩[i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ➡*[h, g] T1 &
+                                   ⇧[0, i+1] T1 ≡ T2.
 #h #g #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
@@ -63,10 +66,10 @@ qed-.
 (* Relocation properties ****************************************************)
 
 lemma cpxs_lift: ∀h,g,G. l_liftable (cpxs h g G).
-/3 width=9 by cpx_lift, cpxs_strap1, l_liftable_LTC/ qed.
+/3 width=10 by cpx_lift, cpxs_strap1, l_liftable_LTC/ qed.
 
 lemma cpxs_inv_lift1: ∀h,g,G. l_deliftable_sn (cpxs h g G).
-/3 width=5 by l_deliftable_sn_LTC, cpx_inv_lift1/
+/3 width=6 by l_deliftable_sn_LTC, cpx_inv_lift1/
 qed-.
 
 (* Properties on supclosure *************************************************)