milestone update in basic_2, update in ground and static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpx_drops.ma

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 5b9970d0fa3f5cde4d6cff50564e56752d90e7f4..686dfe0ad3659b393cf0515ee4f1b9e9a283bcd8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma
@@ -16,61 +16,62 @@ include "ground/xoa/ex_4_5.ma".
 include "basic_2/rt_transition/cpg_drops.ma".
 include "basic_2/rt_transition/cpx.ma".
 
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
+(* EXTENDED 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.
-#h * #G #L #K #V #V2 #W2 #i #HLK *
+lemma cpx_delta_drops (G) (L):
+      ∀I,K,V,V2,W2,i.
+      ⇩[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⬈ V2 →
+      ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈ W2.
+#G #L * #K #V #V2 #W2 #i #HLK *
 /3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
 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 = ⋆(⫯[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/
+lemma cpx_inv_atom1_drops (G) (L):
+      ∀I,T2. ❪G,L❫ ⊢ ⓪[I] ⬈ T2 →
+      ∨∨ T2 = ⓪[I]
+       | ∃∃s1,s2. T2 = ⋆s2 & I = Sort s1
+       | ∃∃J,K,V,V2,i. ⇩[i] L ≘ K.ⓑ[J]V & ❪G,K❫ ⊢ V ⬈ V2 & ⇧[↑i] V2 ≘ T2 & I = LRef i.
+#G #L #I #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
+/4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_2_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 →
-                           T2 = #i ∨
-                           ∃∃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 *
+lemma cpx_inv_lref1_drops (G) (L):
+      ∀T2,i. ❪G,L❫ ⊢ #i ⬈ T2 →
+      ∨∨ T2 = #i 
+       | ∃∃J,K,V,V2. ⇩[i] L ≘ K. ⓑ[J]V & ❪G,K❫ ⊢ V ⬈ V2 & ⇧[↑i] V2 ≘ T2.
+#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-.
 
 (* Properties with generic slicing for local environments *******************)
 
 (* Basic_2A1: includes: cpx_lift *)
-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
+lemma cpx_lifts_sn (G): d_liftable2_sn … lifts (cpx G).
+#G #K #T1 #T2 * #cT #HT12 #b #f #L #HLK #U1 #HTU1
 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/
+lemma cpx_lifts_bi (G): d_liftable2_bi … lifts (cpx G).
+#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_sn: ∀h,G. d_deliftable2_sn … lifts (cpx h G).
-#h #G #L #U1 #U2 * #cU #HU12 #b #f #K #HLK #T1 #HTU1
+lemma cpx_inv_lifts_sn (G): d_deliftable2_sn … lifts (cpx G).
+#G #L #U1 #U2 * #cU #HU12 #b #f #K #HLK #T1 #HTU1
 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/
+lemma cpx_inv_lifts_bi (G): d_deliftable2_bi …lifts (cpx G).
+#G #L #U1 #U2 * /3 width=10 by cpg_inv_lifts_bi, ex_intro/
 qed-.