renaming in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
index c3e2e20658368c7d0185d4dbbd60f891b2b7b3dd..279ee212eb6529b2ea9abd5c092f47d1ea9f3c8a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
@@ -12,33 +12,34 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/syntax/tdeq_tdeq.ma".
+include "basic_2/rt_transition/rpx_rdeq.ma".
 include "basic_2/rt_computation/cpxs.ma".
-include "basic_2/rt_transition/cpx_lfdeq.ma".
-include "basic_2/rt_transition/lfpx_fqup.ma".
 
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
-lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≡[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → 
-                       ∃∃U2.  ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≡[h, o] T2.
+(* Properties with degree-based equivalence for terms ***********************)
+
+lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≛[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → 
+                       ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛[h, o] T2.
 #h #o #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
 #T #T2 #_ #HT2 * #U #HU1 #HUT elim (tdeq_cpx_trans … HUT … HT2) -T -T1
 /3 width=3 by ex2_intro, cpxs_strap1/
 qed-.
 
 (* Note: this requires tdeq to be symmetric *)
-lemma cpxs_tdneq_inv_step_sn: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≡[h, o] T2 → ⊥) →
-                              ∃∃T,T0. ⦃G, L⦄ ⊢ T1 ⬈[h] T & T1 ≡[h, o] T → ⊥ & ⦃G, L⦄ ⊢ T ⬈*[h] T0 & T0 ≡[h, o] T2.
+(* Nasic_2A1: uses: cpxs_neq_inv_step_sn *)
+lemma cpxs_tdneq_fwd_step_sn: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) →
+                              ∃∃T,T0. ⦃G, L⦄ ⊢ T1 ⬈[h] T & T1 ≛[h, o] T → ⊥ & ⦃G, L⦄ ⊢ T ⬈*[h] T0 & T0 ≛[h, o] T2.
 #h #o #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
 [ #H elim H -H //
-| #T1 #T #H1 #H2 #IH #Hn12 elim (tdeq_dec h o T1 T) #H destruct
-  [ -H1 -H2 elim IH -IH /3 width=3 by tdeq_trans/ -Hn12
-    #X #X2 #HTX #HnTX #HX2 #HXT2 elim (tdeq_cpx_trans … H … HTX) -HTX
-    #X1 #HTX1 #HX1 elim (tdeq_cpxs_trans … HX1 … HX2) -HX2
-    /5 width=8 by tdeq_canc_sn, tdeq_trans, ex4_2_intro/ (* Note: 2 tdeq_trans *)
-  | -IH -Hn12 /3 width=6 by ex4_2_intro/
+| #T1 #T0 #HT10 #HT02 #IH #Hn12
+  elim (tdeq_dec h o T1 T0) [ -HT10 -HT02 #H10 | -IH #Hn10 ]
+  [ elim IH -IH /3 width=3 by tdeq_trans/ -Hn12
+    #T3 #T4 #HT03 #Hn03 #HT34 #H42
+    elim (tdeq_cpx_trans … H10 … HT03) -HT03 #T5 #HT15 #H53
+    elim (tdeq_cpxs_trans … H53 … HT34) -HT34 #T6 #HT56 #H64
+    /5 width=8 by tdeq_canc_sn, (* 2x *) tdeq_trans, ex4_2_intro/
+  | /3 width=6 by ex4_2_intro/
   ]
 ]
 qed-.
-
-(* Basic_2A1: removed theorems 1: cpxs_neq_inv_step_sn *)