- some renaming and minor updates

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / csx_tstc_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_tstc_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_tstc_vector.ma
index 765bece71a982647a09bc3d42b1dd5a37dd74e53..736b21f3bf141ba7817942c0dda7c07343deae46 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_tstc_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_tstc_vector.ma
@@ -21,26 +21,26 @@ include "basic_2/computation/csx_vector.ma".
 
 (* Advanced properties ******************************************************)
 
-(* Basic_1: was just: sn3_appls_lref *)
-lemma csx_appls_cnx: ∀h,g,G,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ →
+(* Basic_1: was just: sn3_applv_lref *)
+lemma csx_applv_cnx: ∀h,g,G,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ →
                      ∀Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Vs → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.T.
 #h #g #G #L #T #H1T #H2T #Vs elim Vs -Vs [ #_ @(cnx_csx … H2T) ] (**) (* /2 width=1/ does not work *)
 #V #Vs #IHV #H
 elim (csxv_inv_cons … H) -H #HV #HVs
-@csx_appl_simple_tstc /2 width=1 by appls_simple/ -IHV -HV -HVs
+@csx_appl_simple_tstc /2 width=1 by applv_simple/ -IHV -HV -HVs
 #X #H #H0
 lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
 elim (H0) -H0 //
 qed.
 
-lemma csx_appls_sort: ∀h,g,G,L,k,Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Vs → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.⋆k.
+lemma csx_applv_sort: ∀h,g,G,L,k,Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Vs → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.⋆k.
 #h #g #G #L #k elim (deg_total h g k)
-#l generalize in match k; -k @(nat_ind_plus … l) -l [ /3 width=6 by csx_appls_cnx, cnx_sort, simple_atom/ ]
+#l generalize in match k; -k @(nat_ind_plus … l) -l [ /3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/ ]
 #l #IHl #k #Hkl lapply (deg_next_SO … Hkl) -Hkl
 #Hkl #Vs elim Vs -Vs /2 width=1 by/
 #V #Vs #IHVs #HVVs
 elim (csxv_inv_cons … HVVs) #HV #HVs
-@csx_appl_simple_tstc /2 width=1 by appls_simple, simple_atom/ -IHVs -HV -HVs
+@csx_appl_simple_tstc /2 width=1 by applv_simple, simple_atom/ -IHVs -HV -HVs
 #X #H #H0
 elim (cpxs_fwd_sort_vector … H) -H #H
 [ elim H0 -H0 //
@@ -48,14 +48,14 @@ elim (cpxs_fwd_sort_vector … H) -H #H
 ]
 qed.
 
-(* Basic_1: was just: sn3_appls_beta *)
-lemma csx_appls_beta: ∀h,g,a,G,L,Vs,V,W,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.ⓓ{a}ⓝW.V.T →
+(* Basic_1: was just: sn3_applv_beta *)
+lemma csx_applv_beta: ∀h,g,a,G,L,Vs,V,W,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.ⓓ{a}ⓝW.V.T →
                       ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs. ⓐV.ⓛ{a}W.T.
 #h #g #a #G #L #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
-@csx_appl_simple_tstc /2 width=1 by appls_simple, simple_flat/ -IHV -HV0 -H2T
+@csx_appl_simple_tstc /2 width=1 by applv_simple, simple_flat/ -IHV -HV0 -H2T
 #X #H #H0
 elim (cpxs_fwd_beta_vector … H) -H #H
 [ -H1T elim H0 -H0 //
@@ -63,7 +63,7 @@ elim (cpxs_fwd_beta_vector … H) -H #H
 ]
 qed.
 
-lemma csx_appls_delta: ∀h,g,I,G,L,K,V1,i. ⇩[i] L ≡ K.ⓑ{I}V1 →
+lemma csx_applv_delta: ∀h,g,I,G,L,K,V1,i. ⇩[i] L ≡ K.ⓑ{I}V1 →
                        ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
                        ∀Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] (ⒶVs.V2) → ⦃G, L⦄ ⊢ ⬊*[h, g] (ⒶVs.#i).
 #h #g #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
@@ -71,7 +71,7 @@ lemma csx_appls_delta: ∀h,g,I,G,L,K,V1,i. ⇩[i] L ≡ K.ⓑ{I}V1 →
 | #V #Vs #IHV #H1T
   lapply (csx_fwd_pair_sn … H1T) #HV
   lapply (csx_fwd_flat_dx … H1T) #H2T
-  @csx_appl_simple_tstc /2 width=1 by appls_simple, simple_atom/ -IHV -HV  -H2T
+  @csx_appl_simple_tstc /2 width=1 by applv_simple, simple_atom/ -IHV -HV  -H2T
   #X #H #H0
   elim (cpxs_fwd_delta_vector … HLK … HV12 … H) -HLK -HV12 -H #H
   [ -H1T elim H0 -H0 //
@@ -80,8 +80,8 @@ lemma csx_appls_delta: ∀h,g,I,G,L,K,V1,i. ⇩[i] L ≡ K.ⓑ{I}V1 →
 ]
 qed.
 
-(* Basic_1: was just: sn3_appls_abbr *)
-lemma csx_appls_theta: ∀h,g,a,G,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
+(* Basic_1: was just: sn3_applv_abbr *)
+lemma csx_applv_theta: ∀h,g,a,G,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
                        ∀V,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⓓ{a}V.ⒶV2s.T →
                        ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶV1s.ⓓ{a}V.T.
 #h #g #a #G #L #V1s #V2s * -V1s -V2s /2 width=1 by/
@@ -99,15 +99,15 @@ elim (cpxs_fwd_theta_vector … (V2@V2s) … H1) -H1 /2 width=1 by liftv_cons/ -
 ]
 qed.
 
-(* Basic_1: was just: sn3_appls_cast *)
-lemma csx_appls_cast: ∀h,g,G,L,Vs,W,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.W → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.T →
+(* Basic_1: was just: sn3_applv_cast *)
+lemma csx_applv_cast: ∀h,g,G,L,Vs,W,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.W → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.T →
                       ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.ⓝW.T.
 #h #g #G #L #Vs elim Vs -Vs /2 width=1 by csx_cast/
 #V #Vs #IHV #W #T #H1W #H1T
 lapply (csx_fwd_pair_sn … H1W) #HV
 lapply (csx_fwd_flat_dx … H1W) #H2W
 lapply (csx_fwd_flat_dx … H1T) #H2T
-@csx_appl_simple_tstc /2 width=1 by appls_simple, simple_flat/ -IHV -HV -H2W -H2T
+@csx_appl_simple_tstc /2 width=1 by applv_simple, simple_flat/ -IHV -HV -H2W -H2T
 #X #H #H0
 elim (cpxs_fwd_cast_vector … H) -H #H
 [ -H1W -H1T elim H0 -H0 //
@@ -119,11 +119,11 @@ qed.
 theorem csx_acr: ∀h,g. acr (cpx h g) (eq …) (csx h g) (λG,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T).
 #h #g @mk_acr //
 [ /2 width=8 by csx_lift/
-| /3 width=1 by csx_appls_cnx/
-|3,4,7: /2 width=1 by csx_appls_beta, csx_appls_sort, csx_appls_cast/
-| /2 width=7 by csx_appls_delta/
+| /3 width=1 by csx_applv_cnx/
+|3,4,7: /2 width=1 by csx_applv_beta, csx_applv_sort, csx_applv_cast/
+| /2 width=7 by csx_applv_delta/
 | #G #L #V1s #V2s #HV12s #a #V #T #H #HV
-  @(csx_appls_theta … HV12s) -HV12s
+  @(csx_applv_theta … HV12s) -HV12s
   @csx_abbr //
 ]
 qed.