notational change of lift, drop, and gget

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lsubc_drop.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_drop.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_drop.ma
index 6aa0c01171f22bddb1d2a99e6df45d68def3e416..404f7f5820f3b498db93c2e918eb5e46cceb6d9b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_drop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_drop.ma
@@ -15,14 +15,14 @@
 include "basic_2/static/aaa_lift.ma".
 include "basic_2/computation/lsubc.ma".
 
-(* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
+(* LOCAL ENVIRONMENT REFINEMENT FOR GENERIC REDUCIBILITY ********************)
 
 (* Properties concerning basic local environment slicing ********************)
 
 (* Basic_1: was: csubc_drop_conf_O *)
 (* Note: the constant 0 can not be generalized *)
-lemma lsubc_drop_O1_trans: â\88\80RP,G,L1,L2. G â\8a¢ L1 â«\83[RP] L2 â\86\92 â\88\80K2,s,e. â\87©[s, 0, e] L2 ≡ K2 →
-                           â\88\83â\88\83K1. â\87©[s, 0, e] L1 ≡ K1 & G ⊢ K1 ⫃[RP] K2.
+lemma lsubc_drop_O1_trans: â\88\80RP,G,L1,L2. G â\8a¢ L1 â«\83[RP] L2 â\86\92 â\88\80K2,s,e. â¬\87[s, 0, e] L2 ≡ K2 →
+                           â\88\83â\88\83K1. â¬\87[s, 0, e] L1 ≡ K1 & G ⊢ K1 ⫃[RP] K2.
 #RP #G #L1 #L2 #H elim H -L1 -L2
 [ #X #s #e #H elim (drop_inv_atom1 … H) -H /4 width=3 by drop_atom, ex2_intro/
 | #I #L1 #L2 #V #_ #IHL12 #X #s #e #H
@@ -34,25 +34,24 @@ lemma lsubc_drop_O1_trans: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀K2,s,e. ⇩
 | #L1 #L2 #V #W #A #HV #H1W #H2W #_ #IHL12 #X #s #e #H
   elim (drop_inv_O1_pair1 … H) -H * #He #H destruct
   [ elim (IHL12 L2 s 0) -IHL12 // #X #H <(drop_inv_O2 … H) -H
-    /3 width=8 by lsubc_abbr, drop_pair, ex2_intro/
+    /3 width=8 by lsubc_beta, drop_pair, ex2_intro/
   | elim (IHL12 … H) -L2 /3 width=3 by drop_drop_lt, ex2_intro/
   ]
 ]
 qed-.
 
 (* Basic_1: was: csubc_drop_conf_rev *)
-lemma drop_lsubc_trans: ∀RR,RS,RP.
-                        acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
-                        ∀G,L1,K1,d,e. ⇩[Ⓕ, d, e] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
-                        ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⇩[Ⓕ, d, e] L2 ≡ K2.
-#RR #RS #RP #Hacp #Hacr #G #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
+lemma drop_lsubc_trans: ∀RR,RS,RP. gcp RR RS RP →
+                        ∀G,L1,K1,d,e. ⬇[Ⓕ, d, e] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
+                        ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇[Ⓕ, d, e] L2 ≡ K2.
+#RR #RS #RP #Hgcp #G #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
 [ #d #e #He #X #H elim (lsubc_inv_atom1 … H) -H
   >He /2 width=3 by ex2_intro/
 | #L1 #I #V1 #X #H
   elim (lsubc_inv_pair1 … H) -H *
   [ #K1 #HLK1 #H destruct /3 width=3 by lsubc_pair, drop_pair, ex2_intro/
   | #K1 #V #W1 #A #HV1 #H1W1 #H2W1 #HLK1 #H1 #H2 #H3 destruct
-    /3 width=4 by lsubc_abbr, drop_pair, ex2_intro/
+    /3 width=4 by lsubc_beta, drop_pair, ex2_intro/
   ]
 | #I #L1 #K1 #V1 #e #_ #IHLK1 #K2 #HK12
   elim (IHLK1 … HK12) -K1 /3 width=5 by lsubc_pair, drop_drop, ex2_intro/
@@ -63,10 +62,9 @@ lemma drop_lsubc_trans: ∀RR,RS,RP.
   | #K2 #V #W2 #A #HV2 #H1W2 #H2W2 #HK12 #H1 #H2 #H3 destruct
     elim (lift_inv_flat1 … HV21) -HV21 #W3 #V3 #HW23 #HV3 #H destruct
     elim (IHLK1 … HK12) #K #HL1K #HK2
-    lapply (aacr_acr … Hacp Hacr A) -Hacp -Hacr #HA
-    lapply (s0 … HA … HV2 … HLK1 HV3) -HV2
-    lapply (s0 … HA … H1W2 … HLK1 HW23) -H1W2
-    /4 width=11 by lsubc_abbr, aaa_lift, drop_skip, ex2_intro/
+    lapply (gcr_lift … Hgcp … HV2 … HLK1 … HV3) -HV2
+    lapply (gcr_lift … Hgcp … H1W2 … HLK1 … HW23) -H1W2
+    /4 width=11 by lsubc_beta, aaa_lift, drop_skip, ex2_intro/
   ]
 ]
 qed-.