update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
index 586c2847f7a6c83b66641bd714504ffd42f0db16..9ed4a0b59acfa35b9975d7644078c4c662393c31 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/cpxs_tdeq.ma".
+include "basic_2/rt_computation/cpxs_teqx.ma".
 include "basic_2/rt_computation/cpxs_cpxs.ma".
 include "basic_2/rt_computation/csx_csx.ma".
 
@@ -22,48 +22,48 @@ include "basic_2/rt_computation/csx_csx.ma".
 
 (* Basic_1: was just: sn3_intro *)
 lemma csx_intro_cpxs: ∀h,G,L,T1.
-                      (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T2â¦\84) →
-                      â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T1â¦\84.
+                      (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªT2â\9d«) →
+                      â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªT1â\9d«.
 /4 width=1 by cpx_cpxs, csx_intro/ qed-.
 
 (* Basic_1: was just: sn3_pr3_trans *)
-lemma csx_cpxs_trans: â\88\80h,G,L,T1. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T1â¦\84 →
-                      â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T2â¦\84.
+lemma csx_cpxs_trans: â\88\80h,G,L,T1. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªT1â\9d« →
+                      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88*[h] T2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªT2â\9d«.
 #h #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2
 /2 width=3 by csx_cpx_trans/
 qed-.
 
 (* Eliminators with unbound context-sensitive rt-computation for terms ******)
 
-lemma csx_ind_cpxs_tdeq: ∀h,G,L. ∀Q:predicate term.
-                         (â\88\80T1. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T1â¦\84 →
-                               (â\88\80T2. â¦\83G, Lâ¦\84 ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+lemma csx_ind_cpxs_teqx: ∀h,G,L. ∀Q:predicate term.
+                         (â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªT1â\9d« →
+                               (â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
                          ) →
-                         â\88\80T1. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T1â¦\84 →
-                         â\88\80T0. â¦\83G, Lâ¦\84 ⊢ T1 ⬈*[h] T0 → ∀T2. T0 ≛ T2 → Q T2.
+                         â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªT1â\9d« →
+                         â\88\80T0. â\9dªG,Lâ\9d« ⊢ T1 ⬈*[h] T0 → ∀T2. T0 ≛ T2 → Q T2.
 #h #G #L #Q #IH #T1 #H @(csx_ind … H) -T1
 #T1 #HT1 #IH1 #T0 #HT10 #T2 #HT02
-@IH -IH /3 width=3 by csx_cpxs_trans, csx_tdeq_trans/ -HT1 #V2 #HTV2 #HnTV2
-lapply (tdeq_tdneq_trans … HT02 … HnTV2) -HnTV2 #H
-elim (tdeq_cpxs_trans … HT02 … HTV2) -T2 #V0 #HTV0 #HV02
-lapply (tdneq_tdeq_canc_dx … H … HV02) -H #HnTV0
-elim (tdeq_dec T1 T0) #H
-[ lapply (tdeq_tdneq_trans … H … HnTV0) -H -HnTV0 #Hn10
+@IH -IH /3 width=3 by csx_cpxs_trans, csx_teqx_trans/ -HT1 #V2 #HTV2 #HnTV2
+lapply (teqx_tneqx_trans … HT02 … HnTV2) -HnTV2 #H
+elim (teqx_cpxs_trans … HT02 … HTV2) -T2 #V0 #HTV0 #HV02
+lapply (tneqx_teqx_canc_dx … H … HV02) -H #HnTV0
+elim (teqx_dec T1 T0) #H
+[ lapply (teqx_tneqx_trans … H … HnTV0) -H -HnTV0 #Hn10
   lapply (cpxs_trans … HT10 … HTV0) -T0 #H10
-  elim (cpxs_tdneq_fwd_step_sn … H10 …  Hn10) -H10 -Hn10
-  /3 width=8 by tdeq_trans/
-| elim (cpxs_tdneq_fwd_step_sn … HT10 … H) -HT10 -H #T #V #HT1 #HnT1 #HTV #HVT0
-  elim (tdeq_cpxs_trans … HVT0 … HTV0) -T0
-  /3 width=8 by cpxs_trans, tdeq_trans/
+  elim (cpxs_tneqx_fwd_step_sn … H10 …  Hn10) -H10 -Hn10
+  /3 width=8 by teqx_trans/
+| elim (cpxs_tneqx_fwd_step_sn … HT10 … H) -HT10 -H #T #V #HT1 #HnT1 #HTV #HVT0
+  elim (teqx_cpxs_trans … HVT0 … HTV0) -T0
+  /3 width=8 by cpxs_trans, teqx_trans/
 ]
 qed-.
 
 (* Basic_2A1: was: csx_ind_alt *)
 lemma csx_ind_cpxs: ∀h,G,L. ∀Q:predicate term.
-                    (â\88\80T1. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T1â¦\84 →
-                          (â\88\80T2. â¦\83G, Lâ¦\84 ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+                    (â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªT1â\9d« →
+                          (â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
                     ) →
-                    â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 →  Q T.
+                    â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« →  Q T.
 #h #G #L #Q #IH #T #HT
-@(csx_ind_cpxs_tdeq … IH … HT) -IH -HT // (**) (* full auto fails *)
+@(csx_ind_cpxs_teqx … IH … HT) -IH -HT // (**) (* full auto fails *)
 qed-.