milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
index 7f472e2ad1d4f0adda0847421e51569bbc0c2a11..793a5184f62b566a2369dcc3c04d27c8dea1b349 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
@@ -16,13 +16,14 @@ include "static_2/relocation/drops_ctc.ma".
 include "basic_2/rt_transition/cpx_drops.ma".
 include "basic_2/rt_computation/cpxs.ma".
 
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+(* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS *************)
 
 (* Advanced properties ******************************************************)
 
-lemma cpxs_delta: ∀h,I,G,K,V1,V2. ❪G,K❫ ⊢ V1 ⬈*[h] V2 →
-                  ∀W2. ⇧[1] V2 ≘ W2 → ❪G,K.ⓑ[I]V1❫ ⊢ #0 ⬈*[h] W2.
-#h #I #G #K #V1 #V2 #H @(cpxs_ind … H) -V2
+lemma cpxs_delta (G) (K):
+      ∀I,V1,V2. ❪G,K❫ ⊢ V1 ⬈* V2 →
+      ∀W2. ⇧[1] V2 ≘ W2 → ❪G,K.ⓑ[I]V1❫ ⊢ #0 ⬈* W2.
+#G #K #I #V1 #V2 #H @(cpxs_ind … H) -V2
 [ /3 width=3 by cpx_cpxs, cpx_delta/
 | #V #V2 #_ #HV2 #IH #W2 #HVW2
   elim (lifts_total V (𝐔❨1❩))
@@ -30,9 +31,10 @@ lemma cpxs_delta: ∀h,I,G,K,V1,V2. ❪G,K❫ ⊢ V1 ⬈*[h] V2 →
 ]
 qed.
 
-lemma cpxs_lref: ∀h,I,G,K,T,i. ❪G,K❫ ⊢ #i ⬈*[h] T →
-                 ∀U. ⇧[1] T ≘ U → ❪G,K.ⓘ[I]❫ ⊢ #↑i ⬈*[h] U.
-#h #I #G #K #T #i #H @(cpxs_ind … H) -T
+lemma cpxs_lref (G) (K):
+      ∀I,T,i. ❪G,K❫ ⊢ #i ⬈* T →
+      ∀U. ⇧[1] T ≘ U → ❪G,K.ⓘ[I]❫ ⊢ #↑i ⬈* U.
+#G #K #I #T #i #H @(cpxs_ind … H) -T
 [ /3 width=3 by cpx_cpxs, cpx_lref/
 | #T0 #T #_ #HT2 #IH #U #HTU
   elim (lifts_total T0 (𝐔❨1❩))
@@ -41,10 +43,10 @@ lemma cpxs_lref: ∀h,I,G,K,T,i. ❪G,K❫ ⊢ #i ⬈*[h] T →
 qed.
 
 (* Basic_2A1: was: cpxs_delta *)
-lemma cpxs_delta_drops: ∀h,I,G,L,K,V1,V2,i.
-                        ⇩[i] L ≘ K.ⓑ[I]V1 → ❪G,K❫ ⊢ V1 ⬈*[h] V2 →
-                        ∀W2. ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈*[h] W2.
-#h #I #G #L #K #V1 #V2 #i #HLK #H @(cpxs_ind … H) -V2
+lemma cpxs_delta_drops (G) (L):
+      ∀I,K,V1,V2,i. ⇩[i] L ≘ K.ⓑ[I]V1 → ❪G,K❫ ⊢ V1 ⬈* V2 →
+      ∀W2. ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈* W2.
+#G #L #I #K #V1 #V2 #i #HLK #H @(cpxs_ind … H) -V2
 [ /3 width=7 by cpx_cpxs, cpx_delta_drops/
 | #V #V2 #_ #HV2 #IH #W2 #HVW2
   elim (lifts_total V (𝐔❨↑i❩))
@@ -54,11 +56,11 @@ qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_zero1: ∀h,G,L,T2. ❪G,L❫ ⊢ #0 ⬈*[h] T2 →
-                      T2 = #0 ∨
-                      ∃∃I,K,V1,V2. ❪G,K❫ ⊢ V1 ⬈*[h] V2 & ⇧[1] V2 ≘ T2 &
-                                   L = K.ⓑ[I]V1.
-#h #G #L #T2 #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
+lemma cpxs_inv_zero1 (G) (L):
+      ∀T2. ❪G,L❫ ⊢ #0 ⬈* T2 →
+      ∨∨ T2 = #0
+       | ∃∃I,K,V1,V2. ❪G,K❫ ⊢ V1 ⬈* V2 & ⇧[1] V2 ≘ T2 & L = K.ⓑ[I]V1.
+#G #L #T2 #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
   elim (cpx_inv_zero1 … HT2) -HT2 /2 width=1 by or_introl/
@@ -69,10 +71,11 @@ lemma cpxs_inv_zero1: ∀h,G,L,T2. ❪G,L❫ ⊢ #0 ⬈*[h] T2 →
 ]
 qed-.
 
-lemma cpxs_inv_lref1: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #↑i ⬈*[h] T2 →
-                      T2 = #(↑i) ∨
-                      ∃∃I,K,T. ❪G,K❫ ⊢ #i ⬈*[h] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I].
-#h #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
+lemma cpxs_inv_lref1 (G) (L):
+      ∀T2,i. ❪G,L❫ ⊢ #↑i ⬈* T2 →
+      ∨∨ T2 = #(↑i)
+       | ∃∃I,K,T. ❪G,K❫ ⊢ #i ⬈* T & ⇧[1] T ≘ T2 & L = K.ⓘ[I].
+#G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
   elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
@@ -84,11 +87,11 @@ lemma cpxs_inv_lref1: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #↑i ⬈*[h] T2 →
 qed-.
 
 (* Basic_2A1: was: cpxs_inv_lref1 *)
-lemma cpxs_inv_lref1_drops: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #i ⬈*[h] T2 →
-                            T2 = #i ∨
-                            ∃∃I,K,V1,T1. ⇩[i] L ≘ K.ⓑ[I]V1 & ❪G,K❫ ⊢ V1 ⬈*[h] T1 &
-                                         ⇧[↑i] T1 ≘ T2.
-#h #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
+lemma cpxs_inv_lref1_drops (G) (L):
+      ∀T2,i. ❪G,L❫ ⊢ #i ⬈* T2 →
+      ∨∨ T2 = #i
+       | ∃∃I,K,V1,T1. ⇩[i] L ≘ K.ⓑ[I]V1 & ❪G,K❫ ⊢ V1 ⬈* T1 & ⇧[↑i] T1 ≘ T2.
+#G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
   elim (cpx_inv_lref1_drops … HT2) -HT2 /2 width=1 by or_introl/
@@ -103,17 +106,21 @@ qed-.
 (* Properties with generic relocation ***************************************)
 
 (* Basic_2A1: includes: cpxs_lift *)
-lemma cpxs_lifts_sn: ∀h,G. d_liftable2_sn … lifts (cpxs h G).
+lemma cpxs_lifts_sn (G):
+      d_liftable2_sn … lifts (cpxs G).
 /3 width=10 by cpx_lifts_sn, cpxs_strap1, d2_liftable_sn_CTC/ qed-.
 
-lemma cpxs_lifts_bi: ∀h,G. d_liftable2_bi … lifts (cpxs h G).
+lemma cpxs_lifts_bi (G):
+      d_liftable2_bi … lifts (cpxs G).
 /3 width=12 by cpxs_lifts_sn, d_liftable2_sn_bi, lifts_mono/ qed-.
 
 (* Inversion lemmas with generic relocation *********************************)
 
 (* Basic_2A1: includes: cpxs_inv_lift1 *)
-lemma cpxs_inv_lifts_sn: ∀h,G. d_deliftable2_sn … lifts (cpxs h G).
+lemma cpxs_inv_lifts_sn (G):
+      d_deliftable2_sn … lifts (cpxs G).
 /3 width=6 by d2_deliftable_sn_CTC, cpx_inv_lifts_sn/ qed-.
 
-lemma cpxs_inv_lifts_bi: ∀h,G. d_deliftable2_bi … lifts (cpxs h G).
+lemma cpxs_inv_lifts_bi (G):
+      d_deliftable2_bi … lifts (cpxs G).
 /3 width=12 by cpxs_inv_lifts_sn, d_deliftable2_sn_bi, lifts_inj/ qed-.