X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpxs_theq.ma;h=4bd1dd0c14cff76f95efd2cc681cf361f6ed3266;hp=d8a6f77a36ab28c29bdaddf67a2be1df35aea6f5;hb=19a25bf176255055193372554437729a6fa1894c;hpb=69592aa1d0c0d122fb09f11cc53bf4c5a1532fdd

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_theq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_theq.ma
index d8a6f77a3..4bd1dd0c1 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_theq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_theq.ma
@@ -12,12 +12,12 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/syntax/theq_tdeq.ma".
+include "static_2/syntax/theq_tdeq.ma".
 include "basic_2/rt_computation/cpxs_lsubr.ma".
 include "basic_2/rt_computation/cpxs_cnx.ma".
-include "basic_2/rt_computation/lfpxs_cpxs.ma".
+include "basic_2/rt_computation/lpxs_cpxs.ma".
 
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
 (* Forward lemmas with head equivalence for terms ***************************)
 
@@ -32,16 +32,15 @@ qed-.
 
 (* Note: probably this is an inversion lemma *)
 (* Basic_2A1: was: cpxs_fwd_delta *)
-lemma cpxs_fwd_delta_drops: ∀h,o,I,G,L,K,V1,i. ⬇*[i] L ≡ K.ⓑ{I}V1 →
-                            ∀V2. ⬆*[⫯i] V1 ≡ V2 →
+lemma cpxs_fwd_delta_drops: ∀h,o,I,G,L,K,V1,i. ⬇*[i] L ≘ K.ⓑ{I}V1 →
+                            ∀V2. ⬆*[↑i] V1 ≘ V2 →
                             ∀U. ⦃G, L⦄ ⊢ #i ⬈*[h] U →
                             #i ⩳[h, o] U ∨ ⦃G, L⦄ ⊢ V2 ⬈*[h] U.
 #h #o #I #G #L #K #V1 #i #HLK #V2 #HV12 #U #H
 elim (cpxs_inv_lref1_drops … H) -H /2 width=1 by or_introl/
 * #I0 #K0 #V0 #U0 #HLK0 #HVU0 #HU0
 lapply (drops_mono … HLK0 … HLK) -HLK0 #H destruct
-elim (cpxs_lifts … HVU0 (Ⓣ) … L … HV12) -HVU0 -HV12 /2 width=3 by drops_isuni_fwd_drop2/ #X #H
-<(lifts_mono … HU0 … H) -U0 -X /2 width=1 by or_intror/
+/4 width=9 by cpxs_lifts_bi, drops_isuni_fwd_drop2, or_intror/
 qed-.
 
 (* Basic_1: was just: pr3_iso_beta *)
@@ -59,13 +58,13 @@ lemma cpxs_fwd_beta: ∀h,o,p,G,L,V,W,T,U. ⦃G, L⦄ ⊢ ⓐV.ⓛ{p}W.T ⬈*[h]
 qed-.
 
 lemma cpxs_fwd_theta: ∀h,o,p,G,L,V1,V,T,U. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}V.T ⬈*[h] U →
-                      ∀V2. ⬆*[1] V1 ≡ V2 → ⓐV1.ⓓ{p}V.T ⩳[h, o] U ∨
+                      ∀V2. ⬆*[1] V1 ≘ V2 → ⓐV1.ⓓ{p}V.T ⩳[h, o] U ∨
                       ⦃G, L⦄ ⊢ ⓓ{p}V.ⓐV2.T ⬈*[h] U.
 #h #o #p #G #L #V1 #V #T #U #H #V2 #HV12
 elim (cpxs_inv_appl1 … H) -H *
 [ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1 by theq_pair, or_introl/
 | #q #W #T0 #HT0 #HU
-  elim (cpxs_inv_abbr1 … HT0) -HT0 *
+  elim (cpxs_inv_abbr1_dx … HT0) -HT0 *
   [ #V3 #T3 #_ #_ #H destruct
   | #X #HT2 #H #H0 destruct
     elim (lifts_inv_bind1 … H) -H #W2 #T2 #HW2 #HT02 #H destruct
@@ -76,14 +75,12 @@ elim (cpxs_inv_appl1 … H) -H *
   ]
 | #q #V3 #V4 #V0 #T0 #HV13 #HV34 #HT0 #HU
   @or_intror @(cpxs_trans … HU) -U (**) (* explicit constructor *)
-  elim (cpxs_inv_abbr1 … HT0) -HT0 *
+  elim (cpxs_inv_abbr1_dx … HT0) -HT0 *
   [ #V5 #T5 #HV5 #HT5 #H destruct
-    elim (cpxs_lifts … HV13 (Ⓣ) … (L.ⓓV) … HV12) -V1 /3 width=1 by drops_refl, drops_drop/ #X #H
-    <(lifts_mono … HV34 … H) -V3 -X /3 width=1 by cpxs_flat, cpxs_bind/
+    /6 width=9 by cpxs_lifts_bi, drops_refl, drops_drop, cpxs_flat, cpxs_bind/
   | #X #HT1 #H #H0 destruct
     elim (lifts_inv_bind1 … H) -H #V5 #T5 #HV05 #HT05 #H destruct
-    elim (cpxs_lifts … HV13 (Ⓣ) … (L.ⓓV0) … HV12) -HV13 /3 width=1 by drops_refl, drops_drop/ #X #H
-    <(lifts_mono … HV34 … H) -V3 -X #HV24
+    lapply (cpxs_lifts_bi … HV13 (Ⓣ) … (L.ⓓV0) … HV12 … HV34) -V3 /3 width=1 by drops_refl, drops_drop/ #HV24
     @(cpxs_trans … (+ⓓV.ⓐV2.ⓓ{q}V5.T5)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T
     @(cpxs_strap2 … (ⓐV1.ⓓ{q}V0.T0)) [ /4 width=7 by cpx_zeta, lifts_bind, lifts_flat/ ] -V -V5 -T5
     @(cpxs_strap2 … (ⓓ{q}V0.ⓐV2.T0)) /3 width=3 by cpxs_pair_sn, cpxs_bind_dx, cpx_theta/