update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 571a8154685126d61a309f77c45d6a7e071a5c35..cab82ac336828398851c2d59bf6843ad36e74672 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
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/cpxs_toeq_vector.ma".
-include "basic_2/rt_computation/csx_simple_toeq.ma".
+include "basic_2/rt_computation/cpxs_teqo_vector.ma".
+include "basic_2/rt_computation/csx_simple_teqo.ma".
 include "basic_2/rt_computation/csx_lsubr.ma".
 include "basic_2/rt_computation/csx_lpx.ma".
 include "basic_2/rt_computation/csx_vector.ma".
@@ -24,13 +24,13 @@ include "basic_2/rt_computation/csx_vector.ma".
 
 (* Basic_1: was just: sn3_appls_beta *)
 lemma csx_applv_beta (h) (G):
-      â\88\80p,L,Vs,V,W,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.â\93\93{p}â\93\9dW.V.Tâ¦\84 →
-      â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.â\93\90V.â\93\9b{p}W.Tâ¦\84.
+      â\88\80p,L,Vs,V,W,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\92¶Vs.â\93\93[p]â\93\9dW.V.Tâ\9d« →
+      â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\92¶Vs.â\93\90V.â\93\9b[p]W.Tâ\9d«.
 #h #G #p #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_toeq /2 width=1 by applv_simple, simple_flat/ -IHV -HV0 -H2T
+@csx_appl_simple_teqo /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 //
@@ -39,15 +39,15 @@ elim (cpxs_fwd_beta_vector … H) -H #H
 qed.
 
 lemma csx_applv_delta_drops (h) (G):
-      â\88\80I,L,K,V1,i. â¬\87*[i] L â\89\98 K.â\93\91{I}V1 →
-      â\88\80V2. â¬\86*[↑i] V1 ≘ V2 →
-      â\88\80Vs. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.V2â¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.#iâ¦\84.
+      â\88\80I,L,K,V1,i. â\87©*[i] L â\89\98 K.â\93\91[I]V1 →
+      â\88\80V2. â\87§*[↑i] V1 ≘ V2 →
+      â\88\80Vs. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\92¶Vs.V2â\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\92¶Vs.#iâ\9d«.
 #h #G #I #L #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
   lapply (csx_fwd_flat_dx … H1T) #H2T
-  @csx_appl_simple_toeq /2 width=1 by applv_simple, simple_atom/ -IHV -HV  -H2T
+  @csx_appl_simple_teqo /2 width=1 by applv_simple, simple_atom/ -IHV -HV  -H2T
   #X #H #H0
   elim (cpxs_fwd_delta_drops_vector … HLK … HV12 … H) -HLK -HV12 -H #H
   [ -H1T elim H0 -H0 //
@@ -58,8 +58,8 @@ qed.
 
 (* Basic_1: was just: sn3_appls_abbr *)
 lemma csx_applv_theta (h) (G):
-      â\88\80p,L,V1b,V2b. â¬\86*[1] V1b ≘ V2b →
-      â\88\80V,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\93{p}V.â\92¶V2b.Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶V1b.â\93\93{p}V.Tâ¦\84.
+      â\88\80p,L,V1b,V2b. â\87§*[1] V1b ≘ V2b →
+      â\88\80V,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\93\93[p]V.â\92¶V2b.Tâ\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\92¶V1b.â\93\93[p]V.Tâ\9d«.
 #h #G #p #L #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
@@ -68,7 +68,7 @@ elim H -V1b -V2b /2 width=3 by csx_appl_theta/
 lapply (csx_appl_theta … H … HW12) -H -HW12 #H
 lapply (csx_fwd_pair_sn … H) #HW1
 lapply (csx_fwd_flat_dx … H) #H1
-@csx_appl_simple_toeq /2 width=3 by simple_flat/ -IHV12b -HW1 -H1 #X #H1 #H2
+@csx_appl_simple_teqo /2 width=3 by simple_flat/ -IHV12b -HW1 -H1 #X #H1 #H2
 elim (cpxs_fwd_theta_vector … (V2⨮V2b) … H1) -H1 /2 width=1 by liftsv_cons/ -HV12b -HV12
 [ -H #H elim H2 -H2 //
 | -H2 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
@@ -77,14 +77,14 @@ qed.
 
 (* Basic_1: was just: sn3_appls_cast *)
 lemma csx_applv_cast (h) (G):
-      â\88\80L,Vs,U. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.Uâ¦\84 →
-      â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.â\93\9dU.Tâ¦\84.
+      â\88\80L,Vs,U. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\92¶Vs.Uâ\9d« →
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\92¶Vs.Tâ\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªâ\92¶Vs.â\93\9dU.Tâ\9d«.
 #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
 lapply (csx_fwd_flat_dx … H1U) #H2U
 lapply (csx_fwd_flat_dx … H1T) #H2T
-@csx_appl_simple_toeq /2 width=1 by applv_simple, simple_flat/ -IHV -HV -H2U -H2T
+@csx_appl_simple_teqo /2 width=1 by applv_simple, simple_flat/ -IHV -HV -H2U -H2T
 #X #H #H0
 elim (cpxs_fwd_cast_vector … H) -H #H
 [ -H1U -H1T elim H0 -H0 //