update in basic_2 and apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma
index 97b4f2c8f442d0242279ea1caf727522c2cbdaa2..6c9f743cbd8e6c4c2ac6dab6c3ef41024d3e93fc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_fquq.ma
@@ -23,8 +23,8 @@ include "basic_2/rt_transition/lpr.ma".
 (* Properties with extended structural successor for closures ***************)
 
 lemma fqu_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
-                                ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h] U2 →
-                                ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h] L & ❪G1,L1❫ ⊢ T1 ➡[h] U1 & ❪G1,L,U1❫ ⬂[b] ❪G2,L2,U2❫.
+                                ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h,0] U2 →
+                                ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h,0] L & ❪G1,L1❫ ⊢ T1 ➡[h,0] U1 & ❪G1,L,U1❫ ⬂[b] ❪G2,L2,U2❫.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ /3 width=5 by lpr_pair, fqu_lref_O, ex3_2_intro/
 | /3 width=5 by cpr_pair_sn, fqu_pair_sn, ex3_2_intro/
@@ -38,8 +38,8 @@ lemma fqu_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G
 qed-.
 
 lemma fqu_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
-                                ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h] U2 →
-                                ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h] L & ❪G1,L❫ ⊢ T1 ➡[h] U1 & ❪G1,L,U1❫ ⬂[b] ❪G2,L2,U2❫.
+                                ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h,0] U2 →
+                                ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h,0] L & ❪G1,L❫ ⊢ T1 ➡[h,0] U1 & ❪G1,L,U1❫ ⬂[b] ❪G2,L2,U2❫.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ /3 width=5 by lpr_pair, fqu_lref_O, ex3_2_intro/
 | /3 width=5 by cpr_pair_sn, fqu_pair_sn, ex3_2_intro/
@@ -53,8 +53,8 @@ lemma fqu_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G
 qed-.
 
 lemma fqu_lpr_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❫.
+                             ∀K2. ❪G2,L2❫ ⊢ ➡[h,0] K2 →
+                             ∃∃K1,T. ❪G1,L1❫ ⊢ ➡[h,0] K1 & ❪G1,L1❫ ⊢ T1 ➡[h,0] 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
 [ /3 width=5 by lpr_bind_refl_dx, fqu_lref_O, ex3_2_intro/
 | /3 width=5 by cpr_pair_sn, fqu_pair_sn, ex3_2_intro/
@@ -72,8 +72,8 @@ qed-.
 (* Note: does not hold in Basic_2A1 because it requires cpm *)
 (* Note: L1 = K0.ⓛV0 and T1 = #0 require n = 1 *)
 lemma lpr_fqu_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
-                             ∀K1. ❪G1,K1❫ ⊢ ➡[h] L1 →
-                             ∃∃n,K2,T. ❪G1,K1❫ ⊢ T1 ➡[n,h] T & ❪G1,K1,T❫ ⬂[b] ❪G2,K2,T2❫ & ❪G2,K2❫ ⊢ ➡[h] L2 & n ≤ 1.
+                             ∀K1. ❪G1,K1❫ ⊢ ➡[h,0] L1 →
+                             ∃∃n,K2,T. ❪G1,K1❫ ⊢ T1 ➡[h,n] T & ❪G1,K1,T❫ ⬂[b] ❪G2,K2,T2❫ & ❪G2,K2❫ ⊢ ➡[h,0] L2 & n ≤ 1.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ * #G #K #V #K1 #H
   elim (lpr_inv_pair_dx … H) -H #K0 #V0 #HK0 #HV0 #H destruct
@@ -92,8 +92,8 @@ qed-.
 (* Properties with extended optional structural successor for closures ******)
 
 lemma fquq_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ →
-                                 ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h] U2 →
-                                 ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h] L & ❪G1,L1❫ ⊢ T1 ➡[h] U1 & ❪G1,L,U1❫ ⬂⸮[b] ❪G2,L2,U2❫.
+                                 ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h,0] U2 →
+                                 ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h,0] L & ❪G1,L1❫ ⊢ T1 ➡[h,0] U1 & ❪G1,L,U1❫ ⬂⸮[b] ❪G2,L2,U2❫.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 cases H -H
 [ #HT12 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
@@ -101,8 +101,8 @@ lemma fquq_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b]
 qed-.
 
 lemma fquq_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ →
-                                 ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h] U2 →
-                                 ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h] L & ❪G1,L❫ ⊢ T1 ➡[h] U1 & ❪G1,L,U1❫ ⬂⸮[b] ❪G2,L2,U2❫.
+                                 ∀U2. ❪G2,L2❫ ⊢ T2 ➡[h,0] U2 →
+                                 ∃∃L,U1. ❪G1,L1❫ ⊢ ➡[h,0] L & ❪G1,L❫ ⊢ T1 ➡[h,0] U1 & ❪G1,L,U1❫ ⬂⸮[b] ❪G2,L2,U2❫.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 cases H -H
 [ #HT12 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
@@ -110,8 +110,8 @@ lemma fquq_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b]
 qed-.
 
 lemma fquq_lpr_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❫.
+                              ∀K2. ❪G2,L2❫ ⊢ ➡[h,0] K2 →
+                              ∃∃K1,T. ❪G1,L1❫ ⊢ ➡[h,0] K1 & ❪G1,L1❫ ⊢ T1 ➡[h,0] T & ❪G1,K1,T❫ ⬂⸮[b] ❪G2,K2,T2❫.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K2 #HLK2 cases H -H
 [ #H12 elim (fqu_lpr_trans … H12 … HLK2) /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
@@ -119,8 +119,8 @@ lemma fquq_lpr_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪
 qed-.
 
 lemma lpr_fquq_trans (h) (b): ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂⸮[b] ❪G2,L2,T2❫ →
-                              ∀K1. ❪G1,K1❫ ⊢ ➡[h] L1 →
-                              ∃∃n,K2,T. ❪G1,K1❫ ⊢ T1 ➡[n,h] T & ❪G1,K1,T❫ ⬂⸮[b] ❪G2,K2,T2❫ & ❪G2,K2❫ ⊢ ➡[h] L2 & n ≤ 1.
+                              ∀K1. ❪G1,K1❫ ⊢ ➡[h,0] L1 →
+                              ∃∃n,K2,T. ❪G1,K1❫ ⊢ T1 ➡[h,n] T & ❪G1,K1,T❫ ⬂⸮[b] ❪G2,K2,T2❫ & ❪G2,K2❫ ⊢ ➡[h,0] L2 & n ≤ 1.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 cases H -H
 [ #H12 elim (lpr_fqu_trans … H12 … HKL1) -L1 /3 width=7 by fqu_fquq, ex4_3_intro/
 | * #H1 #H2 #H3 destruct /2 width=7 by ex4_3_intro/