work in progress ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpx_etc.ma

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
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/      
+*)