milestone update in basic_2, update in ground and static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lpx_fquq.ma

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 23e08858ceda58eeca0fca8fd1a6c22f5255ea54..1198a5fed0346f3898083a413a48ed724bd9467b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_fquq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_fquq.ma
@@ -19,10 +19,11 @@ include "basic_2/rt_transition/lpx.ma".
 
 (* 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
@@ -37,10 +38,11 @@ lemma lpx_fqu_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L
 ]
 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 #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/
 ]