update in staic_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / reqx_fqus.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma
index 6f9b14b420483be25027fb6685a0048c7c529d8c..b5f80fc34c2e18dfdb85a362cfdc71abc085b8d9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma
@@ -21,9 +21,10 @@ include "static_2/static/reqx_reqx.ma".
 
 (* Properties with extended structural successor for closures ***************)
 
-lemma fqu_teqx_conf: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂[b] ❪G2,L2,T1❫ →
-                     ∀U2. U1 ≛ U2 →
-                     ∃∃L,T2. ❪G1,L1,U2❫ ⬂[b] ❪G2,L,T2❫ & L2 ≛[T1] L & T1 ≛ T2.
+lemma fqu_teqx_conf (b):
+      ∀G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂[b] ❪G2,L2,T1❫ →
+      ∀U2. U1 ≛ U2 →
+      ∃∃L,T2. ❪G1,L1,U2❫ ⬂[b] ❪G2,L,T2❫ & L2 ≛[T1] L & T1 ≛ T2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -G1 -G2 -L1 -L2 -U1 -T1
 [ #I #G #L #W #X #H >(teqx_inv_lref1 … H) -X
   /2 width=5 by fqu_lref_O, ex3_2_intro/
@@ -45,22 +46,24 @@ lemma fqu_teqx_conf: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂[b] ❪G2,L2,T1
 ]
 qed-.
 
-lemma teqx_fqu_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂[b] ❪G2,L2,T1❫ →
-                      ∀U2. U2 ≛ U1 →
-                      ∃∃L,T2. ❪G1,L1,U2❫ ⬂[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
+lemma teqx_fqu_trans (b):
+      ∀G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂[b] ❪G2,L2,T1❫ →
+      ∀U2. U2 ≛ U1 →
+      ∃∃L,T2. ❪G1,L1,U2❫ ⬂[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H12 #U2 #HU21
 elim (fqu_teqx_conf … H12 U2) -H12
 /3 width=5 by reqx_sym, teqx_sym, ex3_2_intro/
 qed-.
 
 (* Basic_2A1: uses: lleq_fqu_trans *)
-lemma reqx_fqu_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂[b] ❪G2,K2,U❫ →
-                      ∀L1. L1 ≛[T] L2 →
-                      ∃∃K1,U0. ❪G1,L1,T❫ ⬂[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2.
+lemma reqx_fqu_trans (b):
+      ∀G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂[b] ❪G2,K2,U❫ →
+      ∀L1. L1 ≛[T] L2 →
+      ∃∃K1,U0. ❪G1,L1,T❫ ⬂[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H elim H -G1 -G2 -L2 -K2 -T -U
 [ #I #G #L2 #V2 #L1 #H elim (reqx_inv_zero_pair_dx … H) -H
   #K1 #V1 #HV1 #HV12 #H destruct
-  /3 width=7 by teqx_reqx_conf, fqu_lref_O, ex3_2_intro/
+  /3 width=7 by teqx_reqx_conf_sn, fqu_lref_O, ex3_2_intro/
 | * [ #p ] #I #G #L2 #V #T #L1 #H
   [ elim (reqx_inv_bind … H)
   | elim (reqx_inv_flat … H)
@@ -80,9 +83,10 @@ qed-.
 
 (* Properties with optional structural successor for closures ***************)
 
-lemma teqx_fquq_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂⸮[b] ❪G2,L2,T1❫ →
-                       ∀U2. U2 ≛ U1 →
-                       ∃∃L,T2. ❪G1,L1,U2❫ ⬂⸮[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
+lemma teqx_fquq_trans (b):
+      ∀G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂⸮[b] ❪G2,L2,T1❫ →
+      ∀U2. U2 ≛ U1 →
+      ∃∃L,T2. ❪G1,L1,U2❫ ⬂⸮[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -H
 [ #H #U2 #HU21 elim (teqx_fqu_trans … H … HU21) -U1
   /3 width=5 by fqu_fquq, ex3_2_intro/
@@ -91,9 +95,10 @@ lemma teqx_fquq_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂⸮[b] ❪G2,L2
 qed-.
 
 (* Basic_2A1: was just: lleq_fquq_trans *)
-lemma reqx_fquq_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂⸮[b] ❪G2,K2,U❫ →
-                       ∀L1. L1 ≛[T] L2 →
-                       ∃∃K1,U0. ❪G1,L1,T❫ ⬂⸮[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2.
+lemma reqx_fquq_trans (b):
+      ∀G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂⸮[b] ❪G2,K2,U❫ →
+      ∀L1. L1 ≛[T] L2 →
+      ∃∃K1,U0. ❪G1,L1,T❫ ⬂⸮[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H elim H -H
 [ #H #L1 #HL12 elim (reqx_fqu_trans … H … HL12) -L2 /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
@@ -103,9 +108,10 @@ qed-.
 (* Properties with plus-iterated structural successor for closures **********)
 
 (* Basic_2A1: was just: lleq_fqup_trans *)
-lemma reqx_fqup_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂+[b] ❪G2,K2,U❫ →
-                       ∀L1. L1 ≛[T] L2 →
-                       ∃∃K1,U0. ❪G1,L1,T❫ ⬂+[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2.
+lemma reqx_fqup_trans (b):
+      ∀G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂+[b] ❪G2,K2,U❫ →
+      ∀L1. L1 ≛[T] L2 →
+      ∃∃K1,U0. ❪G1,L1,T❫ ⬂+[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U
 [ #G2 #K2 #U #HTU #L1 #HL12 elim (reqx_fqu_trans … HTU … HL12) -L2
   /3 width=5 by fqu_fqup, ex3_2_intro/
@@ -114,13 +120,14 @@ lemma reqx_fqup_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂+[b] ❪G2,K2,U❫
   elim (reqx_fqu_trans … HU2 … HK0) -K #K1 #U1 #HU1 #HU12 #HK12
   elim (teqx_fqu_trans … HU1 … HU0) -U #K3 #U3 #HU03 #HU31 #HK31
   @(ex3_2_intro … K3 U3) (**) (* full auto too slow *)
-  /3 width=5 by reqx_trans, teqx_reqx_conf, fqup_strap1, teqx_trans/
+  /3 width=5 by reqx_trans, teqx_reqx_conf_sn, fqup_strap1, teqx_trans/
 ]
 qed-.
 
-lemma teqx_fqup_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂+[b] ❪G2,L2,T1❫ →
-                       ∀U2. U2 ≛ U1 →
-                       ∃∃L,T2. ❪G1,L1,U2❫ ⬂+[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
+lemma teqx_fqup_trans (b):
+      ∀G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂+[b] ❪G2,L2,T1❫ →
+      ∀U2. U2 ≛ U1 →
+      ∃∃L,T2. ❪G1,L1,U2❫ ⬂+[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H @(fqup_ind_dx … H) -G1 -L1 -U1
 [ #G1 #L1 #U1 #H #U2 #HU21 elim (teqx_fqu_trans … H … HU21) -U1
   /3 width=5 by fqu_fqup, ex3_2_intro/
@@ -129,16 +136,17 @@ lemma teqx_fqup_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂+[b] ❪G2,L2,T
   lapply (teqx_reqx_div … HTU … HL0) -HL0 #HL0
   elim (IH … HTU) -U #K2 #U1 #H2 #HUT1 #HKL2
   elim (reqx_fqup_trans … H2 … HL0) -L #K #U #H2 #HU1 #HK2
-  lapply (teqx_reqx_conf … HUT1 … HK2) -HK2 #HK2
+  lapply (teqx_reqx_conf_sn … HUT1 … HK2) -HK2 #HK2
   /3 width=7 by reqx_trans, fqup_strap2, teqx_trans, ex3_2_intro/
 ]
 qed-.
 
 (* Properties with star-iterated structural successor for closures **********)
 
-lemma teqx_fqus_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂*[b] ❪G2,L2,T1❫ →
-                       ∀U2. U2 ≛ U1 →
-                       ∃∃L,T2. ❪G1,L1,U2❫ ⬂*[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
+lemma teqx_fqus_trans (b):
+      ∀G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂*[b] ❪G2,L2,T1❫ →
+      ∀U2. U2 ≛ U1 →
+      ∃∃L,T2. ❪G1,L1,U2❫ ⬂*[b] ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H #U2 #HU21 elim(fqus_inv_fqup … H) -H
 [ #H elim (teqx_fqup_trans … H … HU21) -U1 /3 width=5 by fqup_fqus, ex3_2_intro/
 | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
@@ -146,9 +154,10 @@ lemma teqx_fqus_trans: ∀b,G1,G2,L1,L2,U1,T1. ❪G1,L1,U1❫ ⬂*[b] ❪G2,L2,T
 qed-.
 
 (* Basic_2A1: was just: lleq_fqus_trans *)
-lemma reqx_fqus_trans: ∀b,G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂*[b] ❪G2,K2,U❫ →
-                       ∀L1. L1 ≛[T] L2 →
-                       ∃∃K1,U0. ❪G1,L1,T❫ ⬂*[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2.
+lemma reqx_fqus_trans (b):
+      ∀G1,G2,L2,K2,T,U. ❪G1,L2,T❫ ⬂*[b] ❪G2,K2,U❫ →
+      ∀L1. L1 ≛[T] L2 →
+      ∃∃K1,U0. ❪G1,L1,T❫ ⬂*[b] ❪G2,K1,U0❫ & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fqus_inv_fqup … H) -H
 [ #H elim (reqx_fqup_trans … H … HL12) -L2 /3 width=5 by fqup_fqus, ex3_2_intro/
 | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/