update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx_vector.ma
index 2aa49c5bd479b149343012d4d47ffef72b550c52..39779d75a562f9239501eebd7909896b171dd541 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx_vector.ma
@@ -23,10 +23,10 @@ include "basic_2/rt_computation/csx_vector.ma".
 (* Advanced properties ************************************* ****************)
 
 (* Basic_1: was just: sn3_appls_beta *)
-lemma csx_applv_beta (h) (G):
-      ∀p,L,Vs,V,W,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.ⓓ[p]ⓝW.V.T❫ →
-      ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.ⓐV.ⓛ[p]W.T❫.
-#h #G #p #L #Vs elim Vs -Vs /2 width=1 by csx_appl_beta/
+lemma csx_applv_beta (h) (G) (L):
+      ∀p,Vs,V,W,T. ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.ⓓ[p]ⓝW.V.T →
+      ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.ⓐV.ⓛ[p]W.T.
+#h #G #L #p #Vs elim Vs -Vs /2 width=1 by csx_appl_beta/
 #V0 #Vs #IHV #V #W #T #H1T
 lapply (csx_fwd_pair_sn … H1T) #HV0
 lapply (csx_fwd_flat_dx … H1T) #H2T
@@ -38,11 +38,11 @@ elim (cpxs_fwd_beta_vector … H) -H #H
 ]
 qed.
 
-lemma csx_applv_delta_drops (h) (G):
-      ∀I,L,K,V1,i. ⇩[i] L ≘ K.ⓑ[I]V1 →
+lemma csx_applv_delta_drops (h) (G) (L):
+      ∀I,K,V1,i. ⇩[i] L ≘ K.ⓑ[I]V1 →
       ∀V2. ⇧[↑i] V1 ≘ V2 →
-      ∀Vs. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.V2❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.#i❫.
-#h #G #I #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
+      ∀Vs. ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.V2 → ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.#i.
+#h #G #L #I #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
 [ /4 width=11 by csx_inv_lifts, csx_lref_pair_drops, drops_isuni_fwd_drop2/
 | #V #Vs #IHV #H1T
   lapply (csx_fwd_pair_sn … H1T) #HV
@@ -57,10 +57,10 @@ lemma csx_applv_delta_drops (h) (G):
 qed.
 
 (* Basic_1: was just: sn3_appls_abbr *)
-lemma csx_applv_theta (h) (G):
-      ∀p,L,V1b,V2b. ⇧[1] V1b ≘ V2b →
-      ∀V,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⓓ[p]V.ⒶV2b.T❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶV1b.ⓓ[p]V.T❫.
-#h #G #p #L #V1b #V2b * -V1b -V2b /2 width=1 by/
+lemma csx_applv_theta (h) (G) (L):
+      ∀p,V1b,V2b. ⇧[1] V1b ≘ V2b →
+      ∀V,T. ❪G,L❫ ⊢ ⬈*𝐒[h] ⓓ[p]V.ⒶV2b.T → ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶV1b.ⓓ[p]V.T.
+#h #G #L #p #V1b #V2b * -V1b -V2b /2 width=1 by/
 #V1b #V2b #V1 #V2 #HV12 #H
 generalize in match HV12; -HV12 generalize in match V2; -V2 generalize in match V1; -V1
 elim H -V1b -V2b /2 width=3 by csx_appl_theta/
@@ -76,9 +76,9 @@ elim (cpxs_fwd_theta_vector … (V2⨮V2b) … H1) -H1 /2 width=1 by liftsv_cons
 qed.
 
 (* Basic_1: was just: sn3_appls_cast *)
-lemma csx_applv_cast (h) (G):
-      ∀L,Vs,U. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.U❫ →
-      ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.T❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.ⓝU.T❫.
+lemma csx_applv_cast (h) (G) (L):
+      ∀Vs,U. ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.U →
+      ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.T → ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.ⓝU.T.
 #h #G #L #Vs elim Vs -Vs /2 width=1 by csx_cast/
 #V #Vs #IHV #U #H1U #T #H1T
 lapply (csx_fwd_pair_sn … H1U) #HV