X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flfpx_frees.ma;h=46fd8a2291071096667a73235ec18309b94219ca;hb=52616a7a6a550efd75ed56e7e246132453506002;hp=935109f903b0756bc42e613679da1b3df17201dc;hpb=045c74915022181e288d9a950cc485437b08d002;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma
index 935109f90..46fd8a229 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma
@@ -13,37 +13,20 @@
 (**************************************************************************)
 
 include "basic_2/relocation/drops_lexs.ma".
-include "basic_2/s_computation/fqup_weight.ma".
 include "basic_2/static/frees_drops.ma".
+include "basic_2/static/lsubf_frees.ma".
+include "basic_2/static/lfxs.ma".
 include "basic_2/rt_transition/cpx_drops.ma".
 
 (* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****)
 
 (* Properties with context-sensitive free variables *************************)
 
-axiom pippo: ∀RN,RP,L1,i. ⬇*[Ⓕ, 𝐔❴i❵] L1 ≡ ⋆ → 
-             ∀f,L2. L1 ⦻*[RN, RP, f] L2 →
-             ⬇*[Ⓕ, 𝐔❴i❵] L2 ≡ ⋆.
-(*
-#RN #RP #L1 #i #H1 #f #L2 #H2
-lapply (lexs_co_dropable_sn … H1 … H2) // -HL1 -H2
-*)
-
-
-axiom frees_inv_lifts_SO: ∀b,f,L,U. L ⊢ 𝐅*⦃U⦄ ≡ f →
-                          ∀K. ⬇*[b, 𝐔❴1❵] L ≡ K → ∀T. ⬆*[1] T ≡ U →
-                          K ⊢ 𝐅*⦃T⦄ ≡ ⫱f.
-
-axiom frees_pair_flat: ∀L,T,f1,I1,V1. L.ⓑ{I1}V1 ⊢ 𝐅*⦃T⦄ ≡ f1 →
-                       ∀f2,I2,V2. L.ⓑ{I2}V2 ⊢ 𝐅*⦃T⦄ ≡ f2 →
-                       ∀f0. f1 ⋓ f2 ≡ f0 →
-                       ∀I0,I. L.ⓑ{I0}ⓕ{I}V1.V2 ⊢ 𝐅*⦃T⦄ ≡ f0.
-
 (* Basic_2A1: was: lpx_cpx_frees_trans *)
-lemma cpx_frees_trans_lexs: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
-                            ∀L2. L1 ⦻*[cpx h G, cfull, f1] L2 →
-                            ∀T2. ⦃G, L1⦄ ⊢ T1 ⬈[h] T2 →
-                            ∃∃f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ f1.
+lemma cpx_frees_conf_lfpx: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
+                           ∀L2. L1 ⦻*[cpx h G, cfull, f1] L2 →
+                           ∀T2. ⦃G, L1⦄ ⊢ T1 ⬈[h] T2 →
+                           ∃∃f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ f1.
 #h #G #L1 #T1 @(fqup_wf_ind_eq … G L1 T1) -G -L1 -T1
 #G0 #L0 #U0 #IH #G #L1 * *
 [ -IH #s #HG #HL #HU #g1 #H1 #L2 #_ #U2 #H0 destruct
@@ -54,8 +37,8 @@ lemma cpx_frees_trans_lexs: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
   elim (frees_inv_lref_drops … H1) -H1 *
   [ -IH #HL1 #Hg1
     elim (cpx_inv_lref1_drops … H0) -H0
-    [ #H destruct lapply (pippo … HL1 … H2) -HL1 -H2
-      /3 width=3 by frees_lref_atom, sle_refl, ex2_intro/
+    [ #H destruct
+      /5 width=9 by frees_lref_atom, drops_atom2_lexs_conf, coafter_isuni_isid, sle_refl, ex2_intro/
     | * -H2 -Hg1 #I #K1 #V1 #V2 #HLK1
       lapply (drops_TF … HLK1) -HLK1 #HLK1
       lapply (drops_mono … HLK1 … HL1) -L1 #H destruct
@@ -121,13 +104,26 @@ lemma cpx_frees_trans_lexs: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
     lapply (sle_lexs_trans … H2 gW1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12W
     lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T
     lapply (lexs_inv_tl … Abst … HL12T … HW12 ?) // -HL12T #HL12T
+    elim (sor_isfin_ex gV1 gW1) /2 width=3 by frees_fwd_isfin/ #g0 #Hg0 #_
+    lapply (sor_trans2 … Hg1 … HgT0 … Hg0) -Hg1 -HgT0 #Hg1
+    lapply (sor_sym … Hg0) -Hg0 #Hg0
     elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21
     elim (IH … HgW1 … HL12W … HW12) // -HgW1 -HL12W -HW12 #gW2 #HgW2 #HgW21
     elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21
+    elim (sor_isfin_ex gV2 (⫱gT2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #gVT2 #HgVT2 #_
+    elim (lsubf_frees_trans … HgT2 (⫯gVT2) … (L2.ⓓⓝW2.V2))
+    [2: /4 width=4 by lsubf_refl, lsubf_beta, sor_inv_sle_dx, sor_inv_sle_sn, sle_inv_tl_sn/ ]
+    -HgT2 #gT0 #HgT0 #HgT20
     elim (sor_isfin_ex gW2 gV2) /2 width=3 by frees_fwd_isfin/ #gV0 #HgV0 #H
-    elim (sor_isfin_ex gV0 (⫱gT2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ -H #g2 #Hg2 #_
+    elim (sor_isfin_ex gV0 (⫱gT0)) /3 width=3 by frees_fwd_isfin, isfin_tl/ -H #g2 #Hg2 #_
     @(ex2_intro … g2)
-    [ @(frees_bind … Hg2) /2 width=5 by frees_flat/ ]
+    [ @(frees_bind … Hg2) /2 width=5 by frees_flat/
+    | -L2 @(sor_inv_sle … Hg2) -Hg2
+      [ /3 width=11 by sor_inv_sle_sn_trans, monotonic_sle_sor/
+      | @sle_xn_tl [2:|*: // ] @(sle_trans … HgT20) -HgT20
+        /4 width=8 by monotonic_sle_sor, sor_inv_sle_dx_trans, sle_tl, sle_next/
+      ] (**) (* full auto too slow *)
+    ]
   | #p #V2 #V #W1 #W2 #T1 #T2 #HV12 #HV2 #HW12 #HT12 #H0 #H1 #H destruct
     elim (frees_inv_bind … HgT0) -HgT0 #gW1 #gT1 #HgW1 #HgT1 #HgT0
     lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V
@@ -144,15 +140,17 @@ lemma cpx_frees_trans_lexs: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
     elim (sor_isfin_ex gW2 (⫱gV0)) /3 width=3 by frees_fwd_isfin, isfin_tl/ -H #g2 #Hg2 #_
     elim (sor_isfin_ex gW2 gV2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
     lapply (sor_trans2 … Hg2 … (⫱gT2) … Hg) /2 width=1 by sor_tl/ #Hg2
-    lapply (frees_lifts (Ⓣ) … HgV2 … (L2.ⓓW2) … HV2 ??) [4: |*: /3 width=3 by drops_refl, drops_drop/ ] -V2 #HgV
-    lapply (sor_sym … Hg) -Hg #Hg
+    lapply (frees_lifts (Ⓣ) … HgV2 … (L2.ⓓW2) … HV2 ??)
+    [4: lapply (sor_sym … Hg) |*: /3 width=3 by drops_refl, drops_drop/ ] -V2 (**) (* full auto too slow *)
     /4 width=10 by frees_flat, frees_bind, monotonic_sle_sor, sle_tl, ex2_intro/
   ]
 ]
+qed-.
 
-lemma cpx_frees_trans: ∀h,o,G. frees_trans (cpx h o G).
-/2 width=8 by lpx_cpx_frees_trans/ qed-.
+(* Basic_2A1: was: cpx_frees_trans *)
+lemma cpx_frees_conf: ∀h,G. R_frees_confluent (cpx h G).
+/3 width=7 by cpx_frees_conf_lfpx, lexs_refl/ qed-.
 
-lemma lpx_frees_trans: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 →
-                       ∀U,i. L2 ⊢ i ϵ 𝐅*[0]⦃U⦄ → L1 ⊢ i ϵ 𝐅*[0]⦃U⦄.
-/2 width=8 by lpx_cpx_frees_trans/ qed-.
+(* Basic_2A1: was: lpx_frees_trans *)
+lemma lfpx_frees_conf: ∀h,G. lexs_frees_confluent (cpx h G) cfull.
+/2 width=7 by cpx_frees_conf_lfpx/ qed-.