milestone in basic_2

[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 ae3d9a8892e37ac4d46ce87b0732aaf7c25f9c32..586c2847f7a6c83b66641bd714504ffd42f0db16 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
@@ -16,54 +16,54 @@ include "basic_2/rt_computation/cpxs_tdeq.ma".
 include "basic_2/rt_computation/cpxs_cpxs.ma".
 include "basic_2/rt_computation/csx_csx.ma".
 
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
-(* Properties with uncounted context-sensitive rt-computation for terms *****)
+(* Properties with unbound context-sensitive rt-computation for terms *******)
 
 (* Basic_1: was just: sn3_intro *)
-lemma csx_intro_cpxs: ∀h,o,G,L,T1.
-                      (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89¡[h, o] T2 â\86\92 â\8a¥) â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] 𝐒⦃T2⦄) →
-                      ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄.
+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] 𝐒⦃T2⦄) →
+                      ⦃G, L⦄ ⊢ ⬈*[h] 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: ∀h,G,L,T1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
+                      ∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T2⦄.
+#h #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2
 /2 width=3 by csx_cpx_trans/
 qed-.
 
-(* Eliminators with uncounted context-sensitive rt-computation for terms ****)
+(* Eliminators with unbound 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⦄ →
-                               (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89¡[h, o] T2 â\86\92 â\8a¥) â\86\92 R T2) â\86\92 R T1
+lemma csx_ind_cpxs_tdeq: ∀h,G,L. ∀Q:predicate term.
+                         (∀T1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃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 Q T2) â\86\92 Q T1
                          ) →
-                         ∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                         â\88\80T0. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T0 â\86\92 â\88\80T2. T0 â\89¡[h, o] T2 â\86\92 R T2.
-#h #o #G #L #R #IH #T1 #H @(csx_ind … H) -T1
+                         ∀T1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
+                         â\88\80T0. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T0 â\86\92 â\88\80T2. T0 â\89\9b T2 â\86\92 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 (tndeq_tdeq_canc_dx … H … HV02) -H #HnTV0
-elim (tdeq_dec h o T1 T0) #H
+lapply (tdneq_tdeq_canc_dx … H … HV02) -H #HnTV0
+elim (tdeq_dec T1 T0) #H
 [ lapply (tdeq_tdneq_trans … H … HnTV0) -H -HnTV0 #Hn10
   lapply (cpxs_trans … HT10 … HTV0) -T0 #H10
-  elim (cpxs_tdneq_inv_step_sn … H10 …  Hn10) -H10 -Hn10
+  elim (cpxs_tdneq_fwd_step_sn … H10 …  Hn10) -H10 -Hn10
   /3 width=8 by tdeq_trans/
-| elim (cpxs_tdneq_inv_step_sn … HT10 … H) -HT10 -H #T #V #HT1 #HnT1 #HTV #HVT0
+| 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/
 ]
 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⦄ →
-                          (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89¡[h, o] T2 â\86\92 â\8a¥) â\86\92 R T2) â\86\92 R T1
+lemma csx_ind_cpxs: ∀h,G,L. ∀Q:predicate term.
+                    (∀T1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃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 Q T2) â\86\92 Q T1
                     ) →
-                    ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R T.
-#h #o #G #L #R #IH #T #HT
+                    ∀T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →  Q T.
+#h #G #L #Q #IH #T #HT
 @(csx_ind_cpxs_tdeq … IH … HT) -IH -HT // (**) (* full auto fails *)
 qed-.