X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcsx_cpxs.ma;h=baba7a13128c28adadd4d7e6ed848e26af54f665;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hp=cfc4d6314e2e6890394e5385181c96ecfdddc299;hpb=f129bbbfda0e65a5f92ec086246f6e288376d4f9;p=helm.git

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 cfc4d6314..baba7a131 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
@@ -12,58 +12,60 @@
 (*                                                                        *)
 (**************************************************************************)
 
-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".
 
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
 
-(* Properties with unbound context-sensitive rt-computation for terms *******)
+(* Properties with extended context-sensitive rt-computation for terms ******)
 
 (* Basic_1: was just: sn3_intro *)
-lemma csx_intro_cpxs: ∀h,o,G,L,T1.
-                      (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄) →
-                      ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄.
+lemma csx_intro_cpxs (G) (L):
+      ∀T1. (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒 T2) →
+      ❪G,L❫ ⊢ ⬈*𝐒 T1.
 /4 width=1 by cpx_cpxs, csx_intro/ qed-.
 
 (* Basic_1: was just: sn3_pr3_trans *)
-lemma csx_cpxs_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                      ∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
-#h #o #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2
+lemma csx_cpxs_trans (G) (L):
+      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+      ∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → ❪G,L❫ ⊢ ⬈*𝐒 T2.
+#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 ******)
+(* Eliminators with extended context-sensitive rt-computation for terms *****)
 
-lemma csx_ind_cpxs_tdeq: ∀h,o,G,L. ∀R:predicate term.
-                         (∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                               (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
-                         ) →
-                         ∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                         ∀T0. ⦃G, L⦄ ⊢ T1 ⬈*[h] T0 → ∀T2. T0 ≛[h, o] T2 → R T2.
-#h #o #G #L #R #IH #T1 #H @(csx_ind … H) -T1
+lemma csx_ind_cpxs_teqx (G) (L):
+      ∀Q:predicate term.
+      (∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+      ) →
+      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+      ∀T0. ❪G,L❫ ⊢ T1 ⬈* T0 → ∀T2. T0 ≛ T2 → Q T2.
+#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 h o 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,o,G,L. ∀R:predicate term.
-                    (∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                          (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
-                    ) →
-                    ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R T.
-#h #o #G #L #R #IH #T #HT
-@(csx_ind_cpxs_tdeq … IH … HT) -IH -HT // (**) (* full auto fails *)
+lemma csx_ind_cpxs (G) (L) (Q:predicate …):
+      (∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+      ) →
+      ∀T. ❪G,L❫ ⊢ ⬈*𝐒 T → Q T.
+#G #L #Q #IH #T #HT
+@(csx_ind_cpxs_teqx … IH … HT) -IH -HT // (**) (* full auto fails *)
 qed-.