work in progress ...

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
index 0fda037b18022749f623cb821d72d0f7316f7e8a..05f1e7357074d8c951efca0349737f012bc9ce72 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
@@ -1,20 +1,14 @@
 
-include "basic_2/static/lfxs_lfxs.ma".
-include "basic_2/rt_transition/lfpx_frees.ma".
-include "basic_2/rt_computation/lfpxs_fqup.ma".
-
-axiom cpx_frees_conf_lfpxs: ∀h,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈[h] T2 →
-                            ∀f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
-                            ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T1] L2 →
-                            ∀g1. L2 ⊢ 𝐅*⦃T1⦄ ≡ g1 →
-                            ∃∃g2. L2 ⊢ 𝐅*⦃T2⦄ ≡ g2 & g2 ⊆ g1 & g1 ⊆ f1.
+include "basic_2/static/lfxs_lex.ma".
+include "basic_2/static/lfxs_fle.ma".
+include "basic_2/rt_transition/cpx_etc.ma".
+include "basic_2/rt_computation/lfpxs_lpxs.ma".
 
 lemma lfpxs_cpx_conf: ∀h,G. s_r_confluent1 … (cpx h G) (lfpxs h G).
 #h #G #L1 #T1 #T2 #HT12 #L2 #H
-lapply (cpx_frees_conf_lfpxs … HT12) -HT12 #HT12
-@(lfpxs_ind_sn … H) -L2 //
-#L #L2 #HL1 * #g1 #Hg1 #HL2 #IH
-elim (frees_total L1 T1) #f1 #Hf1
-elim (HT12 … Hf1 …  HL1 … Hg1) -T1 #g2 #Hg2 #Hg21 #_ -f1
-/4 width=7 by lfpxs_step_dx, sle_lexs_trans, ex2_intro/
+elim (tc_lfxs_inv_lex_lfeq … H) -H #L #HL1 #HL2
+lapply (lfxs_lex … HL1 T1) #H
+elim (cpx_lfxs_conf_gen … HT12 … H) -HT12 -H // #_ #HT21 #_
+@(lfpxs_lpxs_lfeq … HL1) -HL1
+@(fle_lfxs_trans … HL2) //
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma
new file mode 100644 (file)
index 0000000..7a516ee
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma
@@ -0,0 +1,93 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/static/fle_drops.ma".
+include "basic_2/static/fle_fqup.ma".
+include "basic_2/static/fle_fle.ma".
+include "basic_2/static/lfxs.ma".
+include "basic_2/rt_transition/cpx.ma".
+
+axiom fle_pair_sn: ∀L,V1,V2. ⦃L, V1⦄ ⊆ ⦃L, V2⦄ →
+                   ∀I1,I2,T. ⦃L.ⓑ{I1}V1, T⦄ ⊆ ⦃L.ⓑ{I2}V2, T⦄.
+(*
+axiom fle_elim_flat: ∀L1,L2,V1,T2. ⦃L1, V1⦄ ⊆ ⦃L2, T2⦄ → ∀T1. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →
+                     ∀I. ⦃L1, ⓕ{I}V1.T1⦄ ⊆ ⦃L2, T2⦄.
+
+axiom fle_elim_bind: 
+                     ∀p,I1,I2,J1,J2,L,V,W,T. ⦃L, ⓑ{p,I1}ⓕ{J1}V.W.T⦄ ⊆ ⦃L, ⓕ{J2}V.ⓑ{p,I2}W.T⦄.
+*)
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************)
+
+(* Properties with context-sensitive free variables *************************)
+
+(* Note: "⦃L2, T1⦄ ⊆ ⦃L0, T1⦄" may not hold *)
+axiom cpx_lfxs_conf_gen: ∀R. c_reflexive … R →
+                         ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
+                         ∀L2. L0 ⪤*[R, T0] L2 →
+                         ∧∧ ⦃L2, T0⦄ ⊆ ⦃L0, T0⦄ & ⦃L2, T1⦄ ⊆ ⦃L2, T0⦄
+                          & ⦃L0, T1⦄ ⊆ ⦃L0, T0⦄.
+(*
+#R #HR #h #G #L0 #T0 @(fqup_wf_ind_eq (Ⓕ) … G L0 T0) -G -L0 -T0
+#G #L #T #IH #G0 #L0 * *
+[ #s #HG #HL #HT #X #HX #Y #_ destruct -IH
+  elim (cpx_inv_sort1 … HX) -HX #H destruct
+  /2 width=1 by and3_intro/
+|
+| #l #HG #HL #HT #X #HX #Y #_ destruct -IH
+  >(cpx_inv_gref1 … HX) -X
+  /2 width=1 by and3_intro/
+| #p #I #V0 #T0 #HG #HL #HT #X #HX #Y #HY destruct
+  elim (lfxs_inv_bind … V0 ? HY) -HY // #HV0 #HT0
+  elim (cpx_inv_bind1 … HX) -HX *
+  [ #V1 #T1 #HV01 #HT01 #H destruct
+    elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V
+    elim (IH … HT01 … HT0) -HT01 -HT0 -IH // #H1T #H2T #H3T
+    /5 width=4 by fle_pair_sn, fle_trans, fle_bind, and3_intro/
+  | #T #HT #HXT #H1 #H2 destruct
+    elim (IH G0 … V0… V0 … HV0) -HV0 // #H1V #H2V #H3V
+    elim (IH … HT … HT0) -HT -HT0 -IH // #H1T #H2T #H3T
+    /4 width=7 by fle_bind_dx, fle_trans, fle_bind, and3_intro/
+  ]
+| #I #V0 #X0 #HG #HL #HT #X #HX #Y #HY destruct
+  elim (lfxs_inv_flat … HY) -HY #HV0 #HX0
+  elim (cpx_inv_flat1 … HX) -HX *
+  [ #V1 #T1 #HV01 #HT01 #H destruct
+    elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V
+    elim (IH … HT01 … HX0) -HT01 -HX0 -IH // #H1T #H2T #H3T
+    /3 width=3 by fle_flat, and3_intro/
+  | #HX #H destruct
+    elim (IH G0 … V0… V0 … HV0) -HV0 // #H1V #H2V #H3V
+    elim (IH … HX … HX0) -HX -HX0 -IH // #H1T #H2T #H3T
+    /4 width=4 by fle_trans, fle_flat, and3_intro/
+  | #HX #H destruct
+    elim (IH … HX … HV0) -HX -HV0 // #H1V #H2V #H3V
+    elim (IH G0 … X0… X0 … HX0) -HX0 -IH // #H1T #H2T #H3T
+    /4 width=4 by fle_trans, fle_flat, and3_intro/
+  | #p #V1 #W0 #W1 #T0 #T1 #HV01 #HW01 #HT01 #H1 #H2 #H3 destruct
+    elim (lfxs_inv_bind … W0 ? HX0) -HX0 // #HW0 #HT0
+    elim (IH … HV01 … HV0) -HV01 -HV0 // #H1V #H2V #H3V
+    elim (IH … HW01 … HW0) -HW01 -HW0 // #H1W #H2W #H3W
+    elim (IH … HT01 … HT0) -HT01 -HT0 -IH // #H1T #H2T #H3T
+    @and3_intro
+    [ /3 width=5 by fle_flat, fle_bind/
+    | @(fle_trans)
+      [4: @(fle_flat … H2V) [2: @(fle_bind … H2T) // | skip | @Appl ]
+      |1,2: skip
+      | @(fle_trans) [3: @fle_elim_bind  
+    
+     … H2T) // 
+    
+    // |1,2: skip
+    | /2 width=1 by fle_bind_dx/      
+*)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fle.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fle.ma
index df8aec011757bb343eb3a63b0c2ffe0008581d60..0d851ce6a9626a29052fcff4fd86c4657296d642 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fle.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fle.ma
@@ -12,7 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/frees_frees.ma".
 include "basic_2/static/fle.ma".
 include "basic_2/static/lfxs_lfxs.ma".