X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flpx_fquq.ma;h=1198a5fed0346f3898083a413a48ed724bd9467b;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hp=2df357c9165d51d790f6dd5b263ee17ba35e960c;hpb=05b047be6817f430c8c72fd9b0902df8bb9f579e;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_fquq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_fquq.ma
index 2df357c91..1198a5fed 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_fquq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_fquq.ma
@@ -12,20 +12,21 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/s_transition/fquq.ma".
+include "static_2/s_transition/fquq.ma".
 include "basic_2/rt_transition/lpx.ma".
 
 (* UNBOUND PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS ***************)
 
 (* Properties with extended structural successor for closures ***************)
 
-lemma lpx_fqu_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
-                             ∀K1. ⦃G1, K1⦄ ⊢ ⬈[h] L1 →
-                             ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ⬈[h] T & ⦃G1, K1, T⦄ ⊐[b] ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ⬈[h] L2.
-#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+lemma lpx_fqu_trans (b):
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
+      ∀K1. ❪G1,K1❫ ⊢ ⬈ L1 →
+      ∃∃K2,T. ❪G1,K1❫ ⊢ T1 ⬈ T & ❪G1,K1,T❫ ⬂[b] ❪G2,K2,T2❫ & ❪G2,K2❫ ⊢ ⬈ L2.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #K #V #K1 #H
   elim (lpx_inv_pair_dx … H) -H #K0 #V0 #HK0 #HV0 #H destruct
-  elim (lifts_total V (𝐔❴1❵)) #T #HVT
+  elim (lifts_total V (𝐔❨1❩)) #T #HVT
   /3 width=5 by cpx_delta, fqu_drop, ex3_2_intro/
 | /3 width=5 by cpx_pair_sn, fqu_pair_sn, ex3_2_intro/
 | /3 width=5 by lpx_bind_refl_dx, cpx_pair_sn, fqu_bind_dx, ex3_2_intro/
@@ -37,13 +38,14 @@ lemma lpx_fqu_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2
 ]
 qed-.
 
-lemma fqu_lpx_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
-                             ∀K2. ⦃G2, L2⦄ ⊢ ⬈[h] K2 →
-                             ∃∃K1,T. ⦃G1, L1⦄ ⊢ ⬈[h] K1 & ⦃G1, L1⦄ ⊢ T1 ⬈[h] T & ⦃G1, K1, T⦄ ⊐[b] ⦃G2, K2, T2⦄.
-#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+lemma fqu_lpx_trans (b):
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
+      ∀K2. ❪G2,L2❫ ⊢ ⬈ K2 →
+      ∃∃K1,T. ❪G1,L1❫ ⊢ ⬈ K1 & ❪G1,L1❫ ⊢ T1 ⬈ T & ❪G1,K1,T❫ ⬂[b] ❪G2,K2,T2❫.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ /3 width=5 by lpx_bind_refl_dx, fqu_lref_O, ex3_2_intro/
 | /3 width=5 by cpx_pair_sn, fqu_pair_sn, ex3_2_intro/
-| #p #I #G2 #L2 #V2 #T2 #X #H
+| #p #I #G2 #L2 #V2 #T2 #Hb #X #H
   elim (lpx_inv_pair_sn … H) -H #K2 #W2 #HLK2 #HVW2 #H destruct
   /3 width=5 by cpx_pair_sn, fqu_bind_dx, ex3_2_intro/
 | #p #I #G2 #L2 #V2 #T2 #Hb #X #H
@@ -56,19 +58,21 @@ qed-.
 
 (* Properties with extended optional structural successor for closures ******)
 
-lemma lpx_fquq_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
-                              ∀K1. ⦃G1, K1⦄ ⊢ ⬈[h] L1 →
-                              ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ⬈[h] T & ⦃G1, K1, T⦄ ⊐⸮[b] ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ⬈[h] L2.
-#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 cases H -H
+lemma lpx_fquq_trans (b):
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ →
+      ∀K1. ❪G1,K1❫ ⊢ ⬈ L1 →
+      ∃∃K2,T. ❪G1,K1❫ ⊢ T1 ⬈ T & ❪G1,K1,T❫ ⬂⸮[b] ❪G2,K2,T2❫ & ❪G2,K2❫ ⊢ ⬈ L2.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 cases H -H
 [ #H12 elim (lpx_fqu_trans … H12 … HKL1) -L1 /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
 ]
 qed-.
 
-lemma fquq_lpx_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
-                              ∀K2. ⦃G2, L2⦄ ⊢ ⬈[h] K2 →
-                              ∃∃K1,T. ⦃G1, L1⦄ ⊢ ⬈[h] K1 & ⦃G1, L1⦄ ⊢ T1 ⬈[h] T & ⦃G1, K1, T⦄ ⊐⸮[b] ⦃G2, K2, T2⦄.
-#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K2 #HLK2 cases H -H
+lemma fquq_lpx_trans (b):
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ →
+      ∀K2. ❪G2,L2❫ ⊢ ⬈ K2 →
+      ∃∃K1,T. ❪G1,L1❫ ⊢ ⬈ K1 & ❪G1,L1❫ ⊢ T1 ⬈ T & ❪G1,K1,T❫ ⬂⸮[b] ❪G2,K2,T2❫.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H #K2 #HLK2 cases H -H
 [ #H12 elim (fqu_lpx_trans … H12 … HLK2) /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
 ]