update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 c31e2d0ab08ba08ad5a0f8cee0cb0f6d072f0306..97b4f2c8f442d0242279ea1caf727522c2cbdaa2 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
@@ -22,9 +22,9 @@ include "basic_2/rt_transition/lpr.ma".
 
 (* Properties with extended structural successor for closures ***************)
 
-lemma fqu_cpr_trans_sn (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
-                                â\88\80U2. â¦\83G2,L2â¦\84 ⊢ T2 ➡[h] U2 →
-                                â\88\83â\88\83L,U1. â¦\83G1,L1â¦\84 â\8a¢ â\9e¡[h] L & â¦\83G1,L1â¦\84 â\8a¢ T1 â\9e¡[h] U1 & â¦\83G1,L,U1â¦\84 â¬\82[b] â¦\83G2,L2,U2â¦\84.
+lemma fqu_cpr_trans_sn (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« →
+                                â\88\80U2. â\9dªG2,L2â\9d« ⊢ T2 ➡[h] U2 →
+                                â\88\83â\88\83L,U1. â\9dªG1,L1â\9d« â\8a¢ â\9e¡[h] L & â\9dªG1,L1â\9d« â\8a¢ T1 â\9e¡[h] U1 & â\9dªG1,L,U1â\9d« â¬\82[b] â\9dªG2,L2,U2â\9d«.
 #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/
@@ -32,14 +32,14 @@ lemma fqu_cpr_trans_sn (h) (b): ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂[b] ⦃G
 | /3 width=5 by cpm_bind_unit, fqu_clear, ex3_2_intro/
 | /3 width=5 by cpr_flat, fqu_flat_dx, ex3_2_intro/
 | #I #G #K #U #T #HUT #U2 #HU2
-  elim (cpm_lifts_sn … HU2 (Ⓣ) … (K.ⓘ{I}) … HUT) -U
+  elim (cpm_lifts_sn … HU2 (Ⓣ) … (K.ⓘ[I]) … HUT) -U
   /3 width=5 by lpr_bind_refl_dx, fqu_drop, drops_refl, drops_drop, ex3_2_intro/
 ]
 qed-.
 
-lemma fqu_cpr_trans_dx (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
-                                â\88\80U2. â¦\83G2,L2â¦\84 ⊢ T2 ➡[h] U2 →
-                                â\88\83â\88\83L,U1. â¦\83G1,L1â¦\84 â\8a¢ â\9e¡[h] L & â¦\83G1,Lâ¦\84 â\8a¢ T1 â\9e¡[h] U1 & â¦\83G1,L,U1â¦\84 â¬\82[b] â¦\83G2,L2,U2â¦\84.
+lemma fqu_cpr_trans_dx (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« →
+                                â\88\80U2. â\9dªG2,L2â\9d« ⊢ T2 ➡[h] U2 →
+                                â\88\83â\88\83L,U1. â\9dªG1,L1â\9d« â\8a¢ â\9e¡[h] L & â\9dªG1,Lâ\9d« â\8a¢ T1 â\9e¡[h] U1 & â\9dªG1,L,U1â\9d« â¬\82[b] â\9dªG2,L2,U2â\9d«.
 #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/
@@ -47,14 +47,14 @@ lemma fqu_cpr_trans_dx (h) (b): ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂[b] ⦃G
 | /3 width=5 by cpm_bind_unit, fqu_clear, ex3_2_intro/
 | /3 width=5 by cpr_flat, fqu_flat_dx, ex3_2_intro/
 | #I #G #K #U #T #HUT #U2 #HU2
-  elim (cpm_lifts_sn … HU2 (Ⓣ) … (K.ⓘ{I}) … HUT) -U
+  elim (cpm_lifts_sn … HU2 (Ⓣ) … (K.ⓘ[I]) … HUT) -U
   /3 width=5 by lpr_bind_refl_dx, fqu_drop, drops_refl, drops_drop, ex3_2_intro/
 ]
 qed-.
 
-lemma fqu_lpr_trans (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
-                             â\88\80K2. â¦\83G2,L2â¦\84 ⊢ ➡[h] K2 →
-                             â\88\83â\88\83K1,T. â¦\83G1,L1â¦\84 â\8a¢ â\9e¡[h] K1 & â¦\83G1,L1â¦\84 â\8a¢ T1 â\9e¡[h] T & â¦\83G1,K1,Tâ¦\84 â¬\82[b] â¦\83G2,K2,T2â¦\84.
+lemma fqu_lpr_trans (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« →
+                             â\88\80K2. â\9dªG2,L2â\9d« ⊢ ➡[h] K2 →
+                             â\88\83â\88\83K1,T. â\9dªG1,L1â\9d« â\8a¢ â\9e¡[h] K1 & â\9dªG1,L1â\9d« â\8a¢ T1 â\9e¡[h] T & â\9dªG1,K1,Tâ\9d« â¬\82[b] â\9dªG2,K2,T2â\9d«.
 #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/
@@ -71,13 +71,13 @@ 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): â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
-                             â\88\80K1. â¦\83G1,K1â¦\84 ⊢ ➡[h] L1 →
-                             â\88\83â\88\83n,K2,T. â¦\83G1,K1â¦\84 â\8a¢ T1 â\9e¡[n,h] T & â¦\83G1,K1,Tâ¦\84 â¬\82[b] â¦\83G2,K2,T2â¦\84 & â¦\83G2,K2â¦\84 ⊢ ➡[h] L2 & n ≤ 1.
+lemma lpr_fqu_trans (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« →
+                             â\88\80K1. â\9dªG1,K1â\9d« ⊢ ➡[h] L1 →
+                             â\88\83â\88\83n,K2,T. â\9dªG1,K1â\9d« â\8a¢ T1 â\9e¡[n,h] T & â\9dªG1,K1,Tâ\9d« â¬\82[b] â\9dªG2,K2,T2â\9d« & â\9dªG2,K2â\9d« ⊢ ➡[h] 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
-  elim (lifts_total V (ð\9d\90\94â\9d´1â\9dµ)) #T #HVT
+  elim (lifts_total V (ð\9d\90\94â\9d¨1â\9d©)) #T #HVT
   /3 width=7 by cpm_ell, cpm_delta, fqu_drop, ex4_3_intro/
 | /3 width=7 by cpr_pair_sn, fqu_pair_sn, ex4_3_intro/
 | /3 width=7 by lpr_bind_refl_dx, cpr_pair_sn, fqu_bind_dx, ex4_3_intro/
@@ -91,36 +91,36 @@ qed-.
 
 (* Properties with extended optional structural successor for closures ******)
 
-lemma fquq_cpr_trans_sn (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82⸮[b] â¦\83G2,L2,T2â¦\84 →
-                                 â\88\80U2. â¦\83G2,L2â¦\84 ⊢ T2 ➡[h] U2 →
-                                 â\88\83â\88\83L,U1. â¦\83G1,L1â¦\84 â\8a¢ â\9e¡[h] L & â¦\83G1,L1â¦\84 â\8a¢ T1 â\9e¡[h] U1 & â¦\83G1,L,U1â¦\84 â¬\82⸮[b] â¦\83G2,L2,U2â¦\84.
+lemma fquq_cpr_trans_sn (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82⸮[b] â\9dªG2,L2,T2â\9d« →
+                                 â\88\80U2. â\9dªG2,L2â\9d« ⊢ T2 ➡[h] U2 →
+                                 â\88\83â\88\83L,U1. â\9dªG1,L1â\9d« â\8a¢ â\9e¡[h] L & â\9dªG1,L1â\9d« â\8a¢ T1 â\9e¡[h] U1 & â\9dªG1,L,U1â\9d« â¬\82⸮[b] â\9dªG2,L2,U2â\9d«.
 #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/
 ]
 qed-.
 
-lemma fquq_cpr_trans_dx (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82⸮[b] â¦\83G2,L2,T2â¦\84 →
-                                 â\88\80U2. â¦\83G2,L2â¦\84 ⊢ T2 ➡[h] U2 →
-                                 â\88\83â\88\83L,U1. â¦\83G1,L1â¦\84 â\8a¢ â\9e¡[h] L & â¦\83G1,Lâ¦\84 â\8a¢ T1 â\9e¡[h] U1 & â¦\83G1,L,U1â¦\84 â¬\82⸮[b] â¦\83G2,L2,U2â¦\84.
+lemma fquq_cpr_trans_dx (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82⸮[b] â\9dªG2,L2,T2â\9d« →
+                                 â\88\80U2. â\9dªG2,L2â\9d« ⊢ T2 ➡[h] U2 →
+                                 â\88\83â\88\83L,U1. â\9dªG1,L1â\9d« â\8a¢ â\9e¡[h] L & â\9dªG1,Lâ\9d« â\8a¢ T1 â\9e¡[h] U1 & â\9dªG1,L,U1â\9d« â¬\82⸮[b] â\9dªG2,L2,U2â\9d«.
 #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/
 ]
 qed-.
 
-lemma fquq_lpr_trans (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82⸮[b] â¦\83G2,L2,T2â¦\84 →
-                              â\88\80K2. â¦\83G2,L2â¦\84 ⊢ ➡[h] K2 →
-                              â\88\83â\88\83K1,T. â¦\83G1,L1â¦\84 â\8a¢ â\9e¡[h] K1 & â¦\83G1,L1â¦\84 â\8a¢ T1 â\9e¡[h] T & â¦\83G1,K1,Tâ¦\84 â¬\82⸮[b] â¦\83G2,K2,T2â¦\84.
+lemma fquq_lpr_trans (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82⸮[b] â\9dªG2,L2,T2â\9d« →
+                              â\88\80K2. â\9dªG2,L2â\9d« ⊢ ➡[h] K2 →
+                              â\88\83â\88\83K1,T. â\9dªG1,L1â\9d« â\8a¢ â\9e¡[h] K1 & â\9dªG1,L1â\9d« â\8a¢ T1 â\9e¡[h] T & â\9dªG1,K1,Tâ\9d« â¬\82⸮[b] â\9dªG2,K2,T2â\9d«.
 #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/
 ]
 qed-.
 
-lemma lpr_fquq_trans (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82⸮[b] â¦\83G2,L2,T2â¦\84 →
-                              â\88\80K1. â¦\83G1,K1â¦\84 ⊢ ➡[h] L1 →
-                              â\88\83â\88\83n,K2,T. â¦\83G1,K1â¦\84 â\8a¢ T1 â\9e¡[n,h] T & â¦\83G1,K1,Tâ¦\84 â¬\82⸮[b] â¦\83G2,K2,T2â¦\84 & â¦\83G2,K2â¦\84 ⊢ ➡[h] L2 & n ≤ 1.
+lemma lpr_fquq_trans (h) (b): â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82⸮[b] â\9dªG2,L2,T2â\9d« →
+                              â\88\80K1. â\9dªG1,K1â\9d« ⊢ ➡[h] L1 →
+                              â\88\83â\88\83n,K2,T. â\9dªG1,K1â\9d« â\8a¢ T1 â\9e¡[n,h] T & â\9dªG1,K1,Tâ\9d« â¬\82⸮[b] â\9dªG2,K2,T2â\9d« & â\9dªG2,K2â\9d« ⊢ ➡[h] 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/