milestone update in basic_2, update in ground and static_2

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

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 4a89de6b3e54f50f97efd68ad52352f5ea63c0be..86dc07b45fa41b3723979cb35031ac83b490f35b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
@@ -15,30 +15,30 @@
 include "basic_2/rt_transition/lpx_reqx.ma".
 include "basic_2/rt_computation/csx_drops.ma".
 
-(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
 
 (* Advanced properties ******************************************************)
 
-lemma csx_teqx_trans (h) (G) (L):
-      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
-      ∀T2. T1 ≛ T2 → ❪G,L❫ ⊢ ⬈*𝐒[h] T2.
-#h #G #L #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
+lemma csx_teqx_trans (G) (L):
+      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+      ∀T2. T1 ≛ T2 → ❪G,L❫ ⊢ ⬈*𝐒 T2.
+#G #L #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
 @csx_intro #T1 #HT21 #HnT21 elim (teqx_cpx_trans … HT2 … HT21) -HT21
 /4 width=5 by teqx_repl/
 qed-.
 
-lemma csx_cpx_trans (h) (G) (L):
-      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
-      ∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → ❪G,L❫ ⊢ ⬈*𝐒[h] T2.
-#h #G #L #T1 #H @(csx_ind … H) -T1 #T1 #HT1 #IHT1 #T2 #HLT12
+lemma csx_cpx_trans (G) (L):
+      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+      ∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → ❪G,L❫ ⊢ ⬈*𝐒 T2.
+#G #L #T1 #H @(csx_ind … H) -T1 #T1 #HT1 #IHT1 #T2 #HLT12
 elim (teqx_dec T1 T2) /3 width=4 by csx_teqx_trans/
 qed-.
 
 (* Basic_1: was just: sn3_cast *)
-lemma csx_cast (h) (G) (L):
-      ∀W. ❪G,L❫ ⊢ ⬈*𝐒[h] W →
-      ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ ⬈*𝐒[h] ⓝW.T.
-#h #G #L #W #HW @(csx_ind … HW) -W
+lemma csx_cast (G) (L):
+      ∀W. ❪G,L❫ ⊢ ⬈*𝐒 W →
+      ∀T. ❪G,L❫ ⊢ ⬈*𝐒 T → ❪G,L❫ ⊢ ⬈*𝐒 ⓝW.T.
+#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
@@ -54,10 +54,10 @@ qed.
 
 (* Basic_1: was just: sn3_abbr *)
 (* Basic_2A1: was: csx_lref_bind *)
-lemma csx_lref_pair_drops (h) (G) (L):
+lemma csx_lref_pair_drops (G) (L):
       ∀I,K,V,i. ⇩[i] L ≘ K.ⓑ[I]V →
-      ❪G,K❫ ⊢ ⬈*𝐒[h] V → ❪G,L❫ ⊢ ⬈*𝐒[h] #i.
-#h #G #L #I #K #V #i #HLK #HV
+      ❪G,K❫ ⊢ ⬈*𝐒 V → ❪G,L❫ ⊢ ⬈*𝐒 #i.
+#G #L #I #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
@@ -70,19 +70,19 @@ qed.
 
 (* Basic_1: was: sn3_gen_def *)
 (* Basic_2A1: was: csx_inv_lref_bind *)
-lemma csx_inv_lref_pair_drops (h) (G) (L):
+lemma csx_inv_lref_pair_drops (G) (L):
       ∀I,K,V,i. ⇩[i] L ≘ K.ⓑ[I]V →
-      ❪G,L❫ ⊢ ⬈*𝐒[h] #i → ❪G,K❫ ⊢ ⬈*𝐒[h] V.
-#h #G #L #I #K #V #i #HLK #Hi
+      ❪G,L❫ ⊢ ⬈*𝐒 #i → ❪G,K❫ ⊢ ⬈*𝐒 V.
+#G #L #I #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_drops (h) (G) (L):
-      ∀i. ❪G,L❫ ⊢ ⬈*𝐒[h] #i →
+lemma csx_inv_lref_drops (G) (L):
+      ∀i. ❪G,L❫ ⊢ ⬈*𝐒 #i →
       ∨∨ ⇩*[Ⓕ,𝐔❨i❩] L ≘ ⋆
        | ∃∃I,K. ⇩[i] L ≘ K.ⓤ[I]
-       | ∃∃I,K,V. ⇩[i] L ≘ K.ⓑ[I]V & ❪G,K❫ ⊢ ⬈*𝐒[h] V.
-#h #G #L #i #H elim (drops_F_uni L i) /2 width=1 by or3_intro0/
+       | ∃∃I,K,V. ⇩[i] L ≘ K.ⓑ[I]V & ❪G,K❫ ⊢ ⬈*𝐒 V.
+#G #L #i #H elim (drops_F_uni L i) /2 width=1 by or3_intro0/
 * * /4 width=9 by csx_inv_lref_pair_drops, ex2_3_intro, ex1_2_intro, or3_intro2, or3_intro1/
 qed-.