update in delayd_updating

[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 778ba66811968708ea961416b4ea52e3c12bb429..66fa65d121b7dc61cb57b19f216de7e8e29cb61e 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
@@ -22,36 +22,36 @@ include "basic_2/rt_computation/cpxs_cpxs.ma".
 (* Properties on supclosure *************************************************)
 
 lemma fqu_cpxs_trans (b):
-      â\88\80G1,G2,L1,L2,T2,U2. â\9dªG2,L2â\9d« ⊢ T2 ⬈* 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* U1 & â\9dªG1,L1,U1â\9d« â¬\82[b] â\9dªG2,L2,U2â\9d«.
+      â\88\80G1,G2,L1,L2,T2,U2. â\9d¨G2,L2â\9d© ⊢ T2 ⬈* U2 →
+      â\88\80T1. â\9d¨G1,L1,T1â\9d© â¬\82[b] â\9d¨G2,L2,T2â\9d© →
+      â\88\83â\88\83U1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* U1 & â\9d¨G1,L1,U1â\9d© â¬\82[b] â\9d¨G2,L2,U2â\9d©.
 #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 (b):
-      â\88\80G1,G2,L1,L2,T2,U2. â\9dªG2,L2â\9d« ⊢ T2 ⬈* 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* U1 & â\9dªG1,L1,U1â\9d« â¬\82⸮[b] â\9dªG2,L2,U2â\9d«.
+      â\88\80G1,G2,L1,L2,T2,U2. â\9d¨G2,L2â\9d© ⊢ T2 ⬈* U2 →
+      â\88\80T1. â\9d¨G1,L1,T1â\9d© â¬\82⸮[b] â\9d¨G2,L2,T2â\9d© →
+      â\88\83â\88\83U1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* U1 & â\9d¨G1,L1,U1â\9d© â¬\82⸮[b] â\9d¨G2,L2,U2â\9d©.
 #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 (b):
-      â\88\80G1,G2,L1,L2,T2,U2. â\9dªG2,L2â\9d« ⊢ T2 ⬈* 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* U1 & â\9dªG1,L1,U1â\9d« â¬\82+[b] â\9dªG2,L2,U2â\9d«.
+      â\88\80G1,G2,L1,L2,T2,U2. â\9d¨G2,L2â\9d© ⊢ T2 ⬈* U2 →
+      â\88\80T1. â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d© →
+      â\88\83â\88\83U1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* U1 & â\9d¨G1,L1,U1â\9d© â¬\82+[b] â\9d¨G2,L2,U2â\9d©.
 #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 (b):
-      â\88\80G1,G2,L1,L2,T2,U2. â\9dªG2,L2â\9d« ⊢ T2 ⬈* 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* U1 & â\9dªG1,L1,U1â\9d« â¬\82*[b] â\9dªG2,L2,U2â\9d«.
+      â\88\80G1,G2,L1,L2,T2,U2. â\9d¨G2,L2â\9d© ⊢ T2 ⬈* U2 →
+      â\88\80T1. â\9d¨G1,L1,T1â\9d© â¬\82*[b] â\9d¨G2,L2,T2â\9d© →
+      â\88\83â\88\83U1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* U1 & â\9d¨G1,L1,U1â\9d© â¬\82*[b] â\9d¨G2,L2,U2â\9d©.
 #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/
@@ -59,72 +59,72 @@ qed-.
 
 (* Note: a proof based on fqu_cpx_trans_tneqx might exist *)
 (* Basic_2A1: uses: fqu_cpxs_trans_neq *)
-lemma fqu_cpxs_trans_tneqx (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« â\8a¢ T2 â¬\88* U2 â\86\92 (T2 â\89\9b U2 → ⊥) →
-      â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88* U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â\9dªG1,L1,U1â\9d« â¬\82[b] â\9dªG2,L2,U2â\9d«.
-#b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+lemma fqu_cpxs_trans_tneqg (S) (b):
+      â\88\80G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â¬\82[b] â\9d¨G2,L2,T2â\9d© →
+      â\88\80U2. â\9d¨G2,L2â\9d© â\8a¢ T2 â¬\88* U2 â\86\92 (T2 â\89\9b[S] U2 → ⊥) →
+      â\88\83â\88\83U1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* U1 & T1 â\89\9b[S] U1 â\86\92 â\8a¥ & â\9d¨G1,L1,U1â\9d© â¬\82[b] â\9d¨G2,L2,U2â\9d©.
+#S #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 𝐔❨1❩)
   #U2 #HVU2 @(ex3_intro … U2)
   [1,3: /3 width=7 by cpxs_delta, fqu_drop/
-  | #H lapply (teqx_inv_lref1 … H) -H
+  | #H lapply (teqg_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))
   [1,3: /2 width=4 by fqu_pair_sn, cpxs_pair_sn/
-  | #H elim (teqx_inv_pair … H) -H /2 width=1 by/
+  | #H elim (teqg_inv_pair … H) -H /2 width=1 by/
   ]
 | #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/
+  | #H elim (teqg_inv_pair … H) -H /2 width=1 by/
   ]
 | #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/
+  | #H elim (teqg_inv_pair … H) -H /2 width=1 by/
   ]
 | #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/
+  | #H elim (teqg_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
-  /4 width=6 by fqu_drop, drops_refl, drops_drop, teqx_inv_lifts_bi, ex3_intro/
+  /4 width=6 by fqu_drop, drops_refl, drops_drop, teqg_inv_lifts_bi, ex3_intro/
 ]
 qed-.
 
 (* Basic_2A1: uses: fquq_cpxs_trans_neq *)
-lemma fquq_cpxs_trans_tneqx (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« â\8a¢ T2 â¬\88* U2 â\86\92 (T2 â\89\9b U2 → ⊥) →
-      â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88* U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â\9dªG1,L1,U1â\9d« â¬\82⸮[b] â\9dªG2,L2,U2â\9d«.
-#b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12
-[ #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_tneqx … H12 … HTU2 H) -T2
+lemma fquq_cpxs_trans_tneqg (S) (b):
+      â\88\80G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â¬\82⸮[b] â\9d¨G2,L2,T2â\9d© →
+      â\88\80U2. â\9d¨G2,L2â\9d© â\8a¢ T2 â¬\88* U2 â\86\92 (T2 â\89\9b[S] U2 → ⊥) →
+      â\88\83â\88\83U1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* U1 & T1 â\89\9b[S] U1 â\86\92 â\8a¥ & â\9d¨G1,L1,U1â\9d© â¬\82⸮[b] â\9d¨G2,L2,U2â\9d©.
+#S #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12
+[ #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_tneqg … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
 | * #HG #HL #HT destruct /3 width=4 by ex3_intro/
 ]
 qed-.
 
 (* Basic_2A1: uses: fqup_cpxs_trans_neq *)
-lemma fqup_cpxs_trans_tneqx (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« â\8a¢ T2 â¬\88* U2 â\86\92 (T2 â\89\9b U2 → ⊥) →
-      â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88* U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â\9dªG1,L1,U1â\9d« â¬\82+[b] â\9dªG2,L2,U2â\9d«.
-#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
+lemma fqup_cpxs_trans_tneqg (S) (b):
+      â\88\80G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d© →
+      â\88\80U2. â\9d¨G2,L2â\9d© â\8a¢ T2 â¬\88* U2 â\86\92 (T2 â\89\9b[S] U2 → ⊥) →
+      â\88\83â\88\83U1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* U1 & T1 â\89\9b[S] U1 â\86\92 â\8a¥ & â\9d¨G1,L1,U1â\9d© â¬\82+[b] â\9d¨G2,L2,U2â\9d©.
+#S #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_tneqg … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
 | #G #G1 #L #L1 #T #T1 #H1 #_ #IH12 #U2 #HTU2 #H elim (IH12 … HTU2 H) -T2
-  #U1 #HTU1 #H #H12 elim (fqu_cpxs_trans_tneqx … H1 … HTU1 H) -T1
+  #U1 #HTU1 #H #H12 elim (fqu_cpxs_trans_tneqg … H1 … HTU1 H) -T1
   /3 width=8 by fqup_strap2, ex3_intro/
 ]
 qed-.
 
 (* Basic_2A1: uses: fqus_cpxs_trans_neq *)
-lemma fqus_cpxs_trans_tneqx (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« â\8a¢ T2 â¬\88* U2 â\86\92 (T2 â\89\9b U2 → ⊥) →
-      â\88\83â\88\83U1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88* U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â\9dªG1,L1,U1â\9d« â¬\82*[b] â\9dªG2,L2,U2â\9d«.
-#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
+lemma fqus_cpxs_trans_tneqg (S) (b):
+      â\88\80G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â¬\82*[b] â\9d¨G2,L2,T2â\9d© →
+      â\88\80U2. â\9d¨G2,L2â\9d© â\8a¢ T2 â¬\88* U2 â\86\92 (T2 â\89\9b[S] U2 → ⊥) →
+      â\88\83â\88\83U1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* U1 & T1 â\89\9b[S] U1 â\86\92 â\8a¥ & â\9d¨G1,L1,U1â\9d© â¬\82*[b] â\9d¨G2,L2,U2â\9d©.
+#S #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_fqup … H12) -H12
+[ #H12 elim (fqup_cpxs_trans_tneqg … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/
 | * #HG #HL #HT destruct /3 width=4 by ex3_intro/
 ]