X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fs_computation%2Ffqus_fqup.ma;h=ec70f69d1ad9d9505a76d370dd66444a966bdc29;hb=cc178d85bc4fec05b6a9dd176f338b3275beb3d9;hp=f59fd10aac770645ef49e9a87567e84c7ae54bb9;hpb=a454837a256907d2f83d42ced7be847e10361ea9;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_fqup.ma
index f59fd10aa..ec70f69d1 100644
--- a/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_fqup.ma
@@ -19,14 +19,14 @@ include "static_2/s_computation/fqus.ma".
 
 (* Alternative definition with plus-iterated supclosure *********************)
 
-lemma fqup_fqus: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂+[b] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ⬂*[b] ⦃G2,L2,T2⦄.
+lemma fqup_fqus: ∀b,G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂+[b] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 /3 width=5 by fqus_strap1, fquq_fqus, fqu_fquq/
 qed.
 
 (* Basic_2A1: was: fqus_inv_gen *)
-lemma fqus_inv_fqup: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂*[b] ⦃G2,L2,T2⦄ →
-                     ⦃G1,L1,T1⦄ ⬂+[b] ⦃G2,L2,T2⦄ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
+lemma fqus_inv_fqup: ∀b,G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩ →
+                     ❨G1,L1,T1❩ ⬂+[b] ❨G2,L2,T2❩ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2 //
 #G #G2 #L #L2 #T #T2 #_ *
 [ #H2 * /3 width=5 by fqup_strap1, or_introl/
@@ -37,38 +37,38 @@ qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma fqus_strap1_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1,L1,T1⦄ ⬂*[b] ⦃G,L,T⦄ → ⦃G,L,T⦄ ⬂[b] ⦃G2,L2,T2⦄ →
-                       ⦃G1,L1,T1⦄ ⬂+[b] ⦃G2,L2,T2⦄.
+lemma fqus_strap1_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ❨G1,L1,T1❩ ⬂*[b] ❨G,L,T❩ → ❨G,L,T❩ ⬂[b] ❨G2,L2,T2❩ →
+                       ❨G1,L1,T1❩ ⬂+[b] ❨G2,L2,T2❩.
 #b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_fqup … H1) -H1
 [ /2 width=5 by fqup_strap1/
 | * /2 width=1 by fqu_fqup/
 ]
 qed-.
 
-lemma fqus_strap2_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1,L1,T1⦄ ⬂[b] ⦃G,L,T⦄ → ⦃G,L,T⦄ ⬂*[b] ⦃G2,L2,T2⦄ →
-                       ⦃G1,L1,T1⦄ ⬂+[b] ⦃G2,L2,T2⦄.
+lemma fqus_strap2_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ❨G1,L1,T1❩ ⬂[b] ❨G,L,T❩ → ❨G,L,T❩ ⬂*[b] ❨G2,L2,T2❩ →
+                       ❨G1,L1,T1❩ ⬂+[b] ❨G2,L2,T2❩.
 #b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_fqup … H2) -H2
 [ /2 width=5 by fqup_strap2/
 | * /2 width=1 by fqu_fqup/
 ]
 qed-.
 
-lemma fqus_fqup_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1,L1,T1⦄ ⬂*[b] ⦃G,L,T⦄ → ⦃G,L,T⦄ ⬂+[b] ⦃G2,L2,T2⦄ →
-                       ⦃G1,L1,T1⦄ ⬂+[b] ⦃G2,L2,T2⦄.
+lemma fqus_fqup_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ❨G1,L1,T1❩ ⬂*[b] ❨G,L,T❩ → ❨G,L,T❩ ⬂+[b] ❨G2,L2,T2❩ →
+                       ❨G1,L1,T1❩ ⬂+[b] ❨G2,L2,T2❩.
 #b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 @(fqup_ind … H2) -H2 -G2 -L2 -T2
 /2 width=5 by fqus_strap1_fqu, fqup_strap1/
 qed-.
 
-lemma fqup_fqus_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1,L1,T1⦄ ⬂+[b] ⦃G,L,T⦄ →
-                       ⦃G,L,T⦄ ⬂*[b] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ⬂+[b] ⦃G2,L2,T2⦄.
+lemma fqup_fqus_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ❨G1,L1,T1❩ ⬂+[b] ❨G,L,T❩ →
+                       ❨G,L,T❩ ⬂*[b] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ⬂+[b] ❨G2,L2,T2❩.
 #b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 @(fqup_ind_dx … H1) -H1 -G1 -L1 -T1
 /3 width=5 by fqus_strap2_fqu, fqup_strap2/
 qed-.
 
 (* Advanced inversion lemmas for plus-iterated supclosure *******************)
 
-lemma fqup_inv_step_sn: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂+[b] ⦃G2,L2,T2⦄ →
-                        ∃∃G,L,T. ⦃G1,L1,T1⦄ ⬂[b] ⦃G,L,T⦄ & ⦃G,L,T⦄ ⬂*[b] ⦃G2,L2,T2⦄.
+lemma fqup_inv_step_sn: ∀b,G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂+[b] ❨G2,L2,T2❩ →
+                        ∃∃G,L,T. ❨G1,L1,T1❩ ⬂[b] ❨G,L,T❩ & ❨G,L,T❩ ⬂*[b] ❨G2,L2,T2❩.
 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1 /2 width=5 by ex2_3_intro/
 #G1 #G #L1 #L #T1 #T #H1 #_ * /4 width=9 by fqus_strap2, fqu_fquq, ex2_3_intro/
 qed-.