X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpx_drops.ma;h=6ad56889f432b552f84bdbcd53517a15dac0e3c1;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=fe9afa3a88baf5ee27e8728fae0b4ff0d46eb2b0;hpb=6f06bee3eeb4f718b273f0cca5873e9dc5e758b2;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma
index fe9afa3a8..6ad56889f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma
@@ -12,17 +12,18 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/xoa/ex_4_5.ma".
 include "basic_2/rt_transition/cpg_drops.ma".
 include "basic_2/rt_transition/cpx.ma".
 
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
 
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: was: cpx_delta *)
 lemma cpx_delta_drops: ∀h,I,G,L,K,V,V2,W2,i.
-                       ⬇*[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ⬈[h] V2 →
-                       ⬆*[⫯i] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ⬈[h] W2.
+                       ⇩*[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⬈[h] V2 →
+                       ⇧*[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈[h] W2.
 #h * #G #L #K #V #V2 #W2 #i #HLK *
 /3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
 qed.
@@ -30,20 +31,20 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_2A1: was: cpx_inv_atom1 *)
-lemma cpx_inv_atom1_drops: ∀h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ⬈[h] T2 →
-                           ∨∨ T2 = ⓪{I}
-                            | ∃∃s. T2 = ⋆(next h s) & I = Sort s
-                            | ∃∃J,K,V,V2,i. ⬇*[i] L ≡ K.ⓑ{J}V & ⦃G, K⦄ ⊢ V ⬈[h] V2 &
-                                            ⬆*[⫯i] V2 ≡ T2 & I = LRef i.
+lemma cpx_inv_atom1_drops: ∀h,I,G,L,T2. ❪G,L❫ ⊢ ⓪[I] ⬈[h] T2 →
+                           ∨∨ T2 = ⓪[I]
+                            | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s
+                            | ∃∃J,K,V,V2,i. ⇩*[i] L ≘ K.ⓑ[J]V & ❪G,K❫ ⊢ V ⬈[h] V2 &
+                                            ⇧*[↑i] V2 ≘ T2 & I = LRef i.
 #h #I #G #L #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
 /4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_intro, ex_intro/
 qed-.
 
 (* Basic_2A1: was: cpx_inv_lref1 *)
-lemma cpx_inv_lref1_drops: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ⬈[h] T2 →
+lemma cpx_inv_lref1_drops: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #i ⬈[h] T2 →
                            T2 = #i ∨
-                           ∃∃J,K,V,V2. ⬇*[i] L ≡ K. ⓑ{J}V & ⦃G, K⦄ ⊢ V ⬈[h] V2 &
-                                       ⬆*[⫯i] V2 ≡ T2.
+                           ∃∃J,K,V,V2. ⇩*[i] L ≘ K. ⓑ[J]V & ❪G,K❫ ⊢ V ⬈[h] V2 &
+                                       ⇧*[↑i] V2 ≘ T2.
 #h #G #L #T1 #i * #c #H elim (cpg_inv_lref1_drops … H) -H *
 /4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/
 qed-.
@@ -51,17 +52,25 @@ qed-.
 (* Properties with generic slicing for local environments *******************)
 
 (* Basic_2A1: includes: cpx_lift *)
-lemma cpx_lifts: ∀h,G. d_liftable2 (cpx h G).
+lemma cpx_lifts_sn: ∀h,G. d_liftable2_sn … lifts (cpx h G).
 #h #G #K #T1 #T2 * #cT #HT12 #b #f #L #HLK #U1 #HTU1
-elim (cpg_lifts … HT12 … HLK … HTU1) -K -T1
+elim (cpg_lifts_sn … HT12 … HLK … HTU1) -K -T1
 /3 width=4 by ex2_intro, ex_intro/
 qed-.
 
+lemma cpx_lifts_bi: ∀h,G. d_liftable2_bi … lifts (cpx h G).
+#h #G #K #T1 #T2 * /3 width=10 by cpg_lifts_bi, ex_intro/
+qed-.
+
 (* Inversion lemmas with generic slicing for local environments *************)
 
 (* Basic_2A1: includes: cpx_inv_lift1 *)
-lemma cpx_inv_lifts: ∀h,G. d_deliftable2_sn (cpx h G).
+lemma cpx_inv_lifts_sn: ∀h,G. d_deliftable2_sn … lifts (cpx h G).
 #h #G #L #U1 #U2 * #cU #HU12 #b #f #K #HLK #T1 #HTU1
-elim (cpg_inv_lifts1 … HU12 … HLK … HTU1) -L -U1
+elim (cpg_inv_lifts_sn … HU12 … HLK … HTU1) -L -U1
 /3 width=4 by ex2_intro, ex_intro/
 qed-.
+
+lemma cpx_inv_lifts_bi: ∀h,G. d_deliftable2_bi …lifts (cpx h G).
+#h #G #L #U1 #U2 * /3 width=10 by cpg_inv_lifts_bi, ex_intro/
+qed-.