update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_fqus.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
index eb71bafca9ad6cdde5cc7eafb25064e126405c52..1dd3b59db63d3bfb937afebd3bea918f83bf9135 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
@@ -21,33 +21,33 @@ include "basic_2/rt_computation/cpxs_cpxs.ma".
 
 (* Properties on supclosure *************************************************)
 
-lemma fqu_cpxs_trans: â\88\80h,b,G1,G2,L1,L2,T2,U2. â¦\83G2,L2â¦\84 ⊢ T2 ⬈*[h] U2 →
-                      â\88\80T1. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
-                      â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â¬\82[b] â¦\83G2,L2,U2â¦\84.
+lemma fqu_cpxs_trans: â\88\80h,b,G1,G2,L1,L2,T2,U2. â\9dªG2,L2â\9d« ⊢ T2 ⬈*[h] U2 →
+                      â\88\80T1. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« →
+                      â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] U1 & â\9dªG1,L1,U1â\9d« â¬\82[b] â\9dªG2,L2,U2â\9d«.
 #h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqu_cpx_trans … HT1 … HT2) -T
 #T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fquq_cpxs_trans: â\88\80h,b,G1,G2,L1,L2,T2,U2. â¦\83G2,L2â¦\84 ⊢ T2 ⬈*[h] U2 →
-                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â¬\82⸮[b] â¦\83G2,L2,T2â¦\84 →
-                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â¬\82⸮[b] â¦\83G2,L2,U2â¦\84.
+lemma fquq_cpxs_trans: â\88\80h,b,G1,G2,L1,L2,T2,U2. â\9dªG2,L2â\9d« ⊢ T2 ⬈*[h] U2 →
+                       â\88\80T1. â\9dªG1,L1,T1â\9d« â¬\82⸮[b] â\9dªG2,L2,T2â\9d« →
+                       â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] U1 & â\9dªG1,L1,U1â\9d« â¬\82⸮[b] â\9dªG2,L2,U2â\9d«.
 #h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fquq_cpx_trans … HT1 … HT2) -T
 #T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fqup_cpxs_trans: â\88\80h,b,G1,G2,L1,L2,T2,U2. â¦\83G2,L2â¦\84 ⊢ T2 ⬈*[h] U2 →
-                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 →
-                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â¬\82+[b] â¦\83G2,L2,U2â¦\84.
+lemma fqup_cpxs_trans: â\88\80h,b,G1,G2,L1,L2,T2,U2. â\9dªG2,L2â\9d« ⊢ T2 ⬈*[h] U2 →
+                       â\88\80T1. â\9dªG1,L1,T1â\9d« â¬\82+[b] â\9dªG2,L2,T2â\9d« →
+                       â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] U1 & â\9dªG1,L1,U1â\9d« â¬\82+[b] â\9dªG2,L2,U2â\9d«.
 #h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqup_cpx_trans … HT1 … HT2) -T
 #U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fqus_cpxs_trans: â\88\80h,b,G1,G2,L1,L2,T2,U2. â¦\83G2,L2â¦\84 ⊢ T2 ⬈*[h] U2 →
-                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â¬\82*[b] â¦\83G2,L2,T2â¦\84 →
-                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â¬\82*[b] â¦\83G2,L2,U2â¦\84.
+lemma fqus_cpxs_trans: â\88\80h,b,G1,G2,L1,L2,T2,U2. â\9dªG2,L2â\9d« ⊢ T2 ⬈*[h] U2 →
+                       â\88\80T1. â\9dªG1,L1,T1â\9d« â¬\82*[b] â\9dªG2,L2,T2â\9d« →
+                       â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] U1 & â\9dªG1,L1,U1â\9d« â¬\82*[b] â\9dªG2,L2,U2â\9d«.
 #h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqus_cpx_trans … HT1 … HT2) -T
 #U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
@@ -55,42 +55,42 @@ qed-.
 
 (* Note: a proof based on fqu_cpx_trans_tneqx might exist *)
 (* Basic_2A1: uses: fqu_cpxs_trans_neq *)
-lemma fqu_cpxs_trans_tneqx: â\88\80h,b,G1,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 → (T2 ≛ U2 → ⊥) →
-                            â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â¬\82[b] â¦\83G2,L2,U2â¦\84.
+lemma fqu_cpxs_trans_tneqx: â\88\80h,b,G1,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 → (T2 ≛ U2 → ⊥) →
+                            â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â\9dªG1,L1,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
-[ #I #G #L #V1 #V2 #HV12 #_ elim (lifts_total V2 ð\9d\90\94â\9d´1â\9dµ)
+[ #I #G #L #V1 #V2 #HV12 #_ elim (lifts_total V2 ð\9d\90\94â\9d¨1â\9d©)
   #U2 #HVU2 @(ex3_intro … U2)
   [1,3: /3 width=7 by cpxs_delta, fqu_drop/
   | #H lapply (teqx_inv_lref1 … H) -H
     #H destruct /2 width=5 by lifts_inv_lref2_uni_lt/
   ]
-| #I #G #L #V1 #T #V2 #HV12 #H0 @(ex3_intro … (②{I}V2.T))
+| #I #G #L #V1 #T #V2 #HV12 #H0 @(ex3_intro … (②[I]V2.T))
   [1,3: /2 width=4 by fqu_pair_sn, cpxs_pair_sn/
   | #H elim (teqx_inv_pair … H) -H /2 width=1 by/
   ]
-| #p #I #G #L #V #T1 #Hb #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2))
+| #p #I #G #L #V #T1 #Hb #T2 #HT12 #H0 @(ex3_intro … (ⓑ[p,I]V.T2))
   [1,3: /2 width=4 by fqu_bind_dx, cpxs_bind/
   | #H elim (teqx_inv_pair … H) -H /2 width=1 by/
   ]
-| #p #I #G #L #V #T1 #Hb #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2))
+| #p #I #G #L #V #T1 #Hb #T2 #HT12 #H0 @(ex3_intro … (ⓑ[p,I]V.T2))
   [1,3: /4 width=4 by lsubr_cpxs_trans, cpxs_bind, lsubr_unit, fqu_clear/
   | #H elim (teqx_inv_pair … H) -H /2 width=1 by/
   ]
-| #I #G #L #V #T1 #T2 #HT12 #H0 @(ex3_intro … (ⓕ{I}V.T2))
+| #I #G #L #V #T1 #T2 #HT12 #H0 @(ex3_intro … (ⓕ[I]V.T2))
   [1,3: /2 width=4 by fqu_flat_dx, cpxs_flat/
   | #H elim (teqx_inv_pair … H) -H /2 width=1 by/
   ]
 | #I #G #L #T1 #U1 #HTU1 #T2 #HT12 #H0
-  elim (cpxs_lifts_sn … HT12 (Ⓣ) … (L.ⓘ{I}) … HTU1) -HT12
+  elim (cpxs_lifts_sn … HT12 (Ⓣ) … (L.ⓘ[I]) … HTU1) -HT12
   /4 width=6 by fqu_drop, drops_refl, drops_drop, teqx_inv_lifts_bi, ex3_intro/
 ]
 qed-.
 
 (* Basic_2A1: uses: fquq_cpxs_trans_neq *)
-lemma fquq_cpxs_trans_tneqx: â\88\80h,b,G1,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 → (T2 ≛ U2 → ⊥) →
-                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â¬\82⸮[b] â¦\83G2,L2,U2â¦\84.
+lemma fquq_cpxs_trans_tneqx: â\88\80h,b,G1,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 → (T2 ≛ U2 → ⊥) →
+                             â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â\9dªG1,L1,U1â\9d« â¬\82⸮[b] â\9dªG2,L2,U2â\9d«.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12
 [ #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_tneqx … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
@@ -99,9 +99,9 @@ lemma fquq_cpxs_trans_tneqx: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂⸮[b]
 qed-.
 
 (* Basic_2A1: uses: fqup_cpxs_trans_neq *)
-lemma fqup_cpxs_trans_tneqx: â\88\80h,b,G1,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 → (T2 ≛ U2 → ⊥) →
-                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â¬\82+[b] â¦\83G2,L2,U2â¦\84.
+lemma fqup_cpxs_trans_tneqx: â\88\80h,b,G1,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 → (T2 ≛ U2 → ⊥) →
+                             â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â\9dªG1,L1,U1â\9d« â¬\82+[b] â\9dªG2,L2,U2â\9d«.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
 [ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_tneqx … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -112,9 +112,9 @@ lemma fqup_cpxs_trans_tneqx: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂+[b] 
 qed-.
 
 (* Basic_2A1: uses: fqus_cpxs_trans_neq *)
-lemma fqus_cpxs_trans_tneqx: â\88\80h,b,G1,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 → (T2 ≛ U2 → ⊥) →
-                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â¬\82*[b] â¦\83G2,L2,U2â¦\84.
+lemma fqus_cpxs_trans_tneqx: â\88\80h,b,G1,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 → (T2 ≛ U2 → ⊥) →
+                             â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â\9dªG1,L1,U1â\9d« â¬\82*[b] â\9dªG2,L2,U2â\9d«.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_fqup … H12) -H12
 [ #H12 elim (fqup_cpxs_trans_tneqx … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/