third commutation property on lazy equivalence for

local environments proved, multistep version

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma
new file mode 100644 (file)
index 0000000..dd325e8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma
@@ -0,0 +1,84 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/relocation/lleq_lleq.ma".
+include "basic_2/computation/lpxs_ldrop.ma".
+include "basic_2/computation/lpxs_cpxs.ma".
+
+(* SN EXTENDED PARALLEL COMPUTATION FOR LOCAL ENVIRONMENTS ******************)
+
+(* Properties on lazy equivalence for local environments ********************)
+
+lemma lpxs_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+                           ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ⋕[0, T1] L1 →
+                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ⋕[0, T2] L2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+[ #I #G1 #L1 #V1 #X #H1 #H2 elim (lpxs_inv_pair2 … H1) -H1
+  #K0 #V0 #H1KL1 #_ #H destruct
+  elim (lleq_inv_lref_ge_dx … H2 ? I L1 V1) -H2 //
+  #K1 #H #H2KL1 lapply (ldrop_inv_O2 … H) -H #H destruct
+  /2 width=4 by fqu_lref_O, ex3_intro/
+| * [ #a ] #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H
+  [ elim (lleq_inv_bind … H)
+  | elim (lleq_inv_flat … H)
+  ] -H /2 width=4 by fqu_pair_sn, ex3_intro/
+| #a #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H elim (lleq_inv_bind_O … H) -H
+  /3 width=4 by lpxs_pair, fqu_bind_dx, ex3_intro/
+| #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H elim (lleq_inv_flat … H) -H
+  /2 width=4 by fqu_flat_dx, ex3_intro/
+| #G1 #L1 #L #T1 #U1 #e #HL1 #HTU1 #K1 #H1KL1 #H2KL1
+  elim (ldrop_O1_le (e+1) K1)
+  [ #K #HK1 lapply (lleq_inv_lift_le … H2KL1 … HK1 HL1 … HTU1 ?) -H2KL1 //
+    #H2KL elim (lpxs_ldrop_trans_O1 … H1KL1 … HL1) -L1
+    #K0 #HK10 #H1KL lapply (ldrop_mono … HK10 … HK1) -HK10 #H destruct
+    /3 width=4 by fqu_drop, ex3_intro/
+  | lapply (ldrop_fwd_length_le2 … HL1) -L -T1 -g
+    lapply (lleq_fwd_length … H2KL1) //
+  ]
+]
+qed-.
+
+lemma lpxs_lleq_fquq_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+                            ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ⋕[0, T1] L1 →
+                            ∃∃K2. ⦃G1, K1, T1⦄ ⊃⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ⋕[0, T2] L2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1
+elim (fquq_inv_gen … H) -H
+[ #H elim (lpxs_lleq_fqu_trans … H … H1KL1 H2KL1) -L1
+  /3 width=4 by fqu_fquq, ex3_intro/
+| * #HG #HL #HT destruct /2 width=4 by ex3_intro/
+]
+qed-.
+
+lemma lpxs_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
+                            ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ⋕[0, T1] L1 →
+                            ∃∃K2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ⋕[0, T2] L2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+[ #G2 #L2 #T2 #H #K1 #H1KL1 #H2KL1 elim (lpxs_lleq_fqu_trans … H … H1KL1 H2KL1) -L1
+  /3 width=4 by fqu_fqup, ex3_intro/
+| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #K1 #H1KL1 #H2KL1 elim (IHT1 … H2KL1) // -L1
+  #K #HT1 #H1KL #H2KL elim (lpxs_lleq_fqu_trans … HT2 … H1KL H2KL) -L
+  /3 width=5 by fqup_strap1, ex3_intro/
+]
+qed-.
+
+lemma lpxs_lleq_fqus_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
+                            ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 → K1 ⋕[0, T1] L1 →
+                            ∃∃K2. ⦃G1, K1, T1⦄ ⊃* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 & K2 ⋕[0, T2] L2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1
+elim (fqus_inv_gen … H) -H
+[ #H elim (lpxs_lleq_fqup_trans … H … H1KL1 H2KL1) -L1
+  /3 width=4 by fqup_fqus, ex3_intro/
+| * #HG #HL #HT destruct /2 width=4 by ex3_intro/
+]
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/leq/leq_old.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/leq/leq_old.etc
index 37deba7ac60f5094fbf6786fc6012ae7eb932b4f..52b458ce447374cc3a80b275b89cee1add094083 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/leq/leq_old.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/leq/leq_old.etc
@@ -12,6 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
+axiom- lleq_inv_lref_lt_bi: ∀L1,L2,i,d. L1 ⋕[d, #i] L2 → i < d →
+                           ∀I1,I2,K1,K2,V1,V2. ⇩[0, i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[0, i] L2 ≡ K2.ⓑ{I2}V2 → 
+                           K1 ⋕[d-i-1, V1] K2 ∧ K1 ⋕[d-i-1, V2] K2.
+
 include "Basic-2/grammar/lenv_length.ma".
 
 (* LOCAL ENVIRONMENT EQUALITY ***********************************************)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
index b54c386b99f454a821191d06116017fb47109b5d..fd95e52cd4e52645d810586aacf0846606fcbe05 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
@@ -1,3 +1,17 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
 include "basic_2/relocation/lleq_lleq.ma".
 include "basic_2/reduction/lpx_ldrop.ma".
 

diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index a4130061fa276295a87e24f0dc2afe756fac973e..9d490be1605da0a275d4c985c18349151132d55e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -103,7 +103,7 @@ table {
           }
         ]
         [ { "context-sensitive extended computation" * } {
-             [ "lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )" "lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )" "lpxs_ldrop" + "lpxs_aaa" + "lpxs_cpxs" + "lpxs_lpxs" * ]
+             [ "lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )" "lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )" "lpxs_ldrop" + "lpxs_lleq" + "lpxs_aaa" + "lpxs_cpxs" + "lpxs_lpxs" * ]
              [ "cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpxs_tstc" + "cpxs_tstc_vector" + "cpxs_lift" + "cpxs_lleq" + "cpxs_aaa" + "cpxs_cpxs" * ]
           }
         ]