advances on cpx_lfxs_conf_fle

[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
index a6c77b5c9272d934b41a3dd6d6d45e55be925aea..19999ed9b7953886e359107eb46367080df73829 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_etc.ma
@@ -18,18 +18,29 @@ include "basic_2/static/fle_fle.ma".
 include "basic_2/static/lfxs_length.ma".
 include "basic_2/rt_transition/cpx.ma".
 
+
+lemma fle_zero_bi: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ⦃K1, V1⦄ ⊆ ⦃K2, V2⦄ →
+                   ∀I1,I2. ⦃K1.ⓑ{I1}V1, #O⦄ ⊆ ⦃K2.ⓑ{I2}V2, #O⦄.
+#K1 #K2 #HK #V1 #V2
+* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
+#I1 #I2
+elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
+/3 width=12 by frees_pair, lveq_bind, sle_next, ex4_4_intro/
+qed.
+
 (* 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_fle: ∀R. c_reflexive … R →
-                         ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
+axiom cpx_lfxs_conf_fle: ∀R,h. c_reflexive … R →
+                         (∨∨ (∀G. (cpx h G) = R) | R_fle_compatible R) →
+                         ∀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
+#R #h #H1R #H2R #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 #HY destruct -IH
   lapply (lfxs_fwd_length … HY) -HY #H0
@@ -41,14 +52,35 @@ axiom cpx_lfxs_conf_fle: ∀R. c_reflexive … R →
       elim (lfxs_inv_zero … HY) -HY *
       [ #H1 #H2 destruct -IH /2 width=1 by and3_intro/
       | #I #K0 #K2 #V0 #V2 #HK02 #HV02 #H1 #H2 destruct
-        elim (IH … HK02) [4,5: /2 width=2 by fqu_fqup, fqu_lref_O/ ]
-   
-    lapply (lfxs_fwd_length … HY) -HY #H0
-    /3 width=1 by fle_lref_length, and3_intro/
-  | * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HX  
-
-  elim (lfxs_inv_lref … HY) -HY // #HV0 #HT0
-
+        lapply (lfxs_fwd_length … HK02) #HK
+        elim H2R -H2R #H2R
+        [ <(H2R G0) in HV02; -H2R #HV02
+          elim (IH … HV02 … HK02) /2 width=2 by fqu_fqup, fqu_lref_O/ -IH -HV02 -HK02 #H1V #H2V #_
+          /4 width=1 by fle_trans_tc, fle_zero_bi, and3_intro/
+        | lapply (H2R … HV02 … HK02) -H2R -HV02 -HK02 -IH #HKV20
+          /3 width=1 by fle_zero_bi, and3_intro/
+        ]
+      | #f #I #K0 #K2 #Hf #HK02 #H1 #H2 destruct
+      ]
+    | * #I0 #K0 #V0 #V1 #HV01 #HV1X #H destruct
+      elim (lfxs_inv_zero_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
+    ]
+  | elim (cpx_inv_lref1 … HX) -HX
+    [ #H destruct
+      elim (lfxs_inv_lref … HY) -HY *
+      [ #H0 #H1 destruct /2 width=1 by and3_intro/
+      | #I0 #I2 #K0 #K2 #HK02 #H1 #H2 destruct
+        lapply (lfxs_fwd_length … HK02) #HK
+        elim (IH … HK02) [|*: /2 width=4 by fqu_fqup/ ] -IH -HK02
+        /3 width=5 by and3_intro, fle_lifts_SO/
+      ]
+    | * #I0 #K0 #V1 #HV1 #HV1X #H0 destruct
+      elim (lfxs_inv_lref_bind_sn … HY) -HY #I2 #K2 #HK02 #H destruct
+      lapply (lfxs_fwd_length … HK02) #HK
+      elim (IH … HK02) [|*: /2 width=4 by fqu_fqup/ ] -IH -HV1 -HK02
+      /3 width=5 by fle_lifts_SO, and3_intro/
+    ]
+  ]
 | #l #HG #HL #HT #X #HX #Y #HY destruct -IH
   lapply (lfxs_fwd_length … HY) -HY #H0
   >(cpx_inv_gref1 … HX) -X
@@ -104,4 +136,4 @@ axiom cpx_lfxs_conf_fle: ∀R. c_reflexive … R →
     ]
   ]
 ]
-*)
\ No newline at end of file
+*)