notational change for lexs

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

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 7e184e1a4a64cba6e7f58f9670a1dc15d6b98d90..d949c0a197968c3bdff6ac9977cba478e08320e8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma
@@ -13,7 +13,6 @@
 (**************************************************************************)
 
 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".
@@ -23,27 +22,9 @@ include "basic_2/rt_transition/cpx_drops.ma".
 
 (* 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 *)
+(* Basic_2A1: uses: lpx_cpx_frees_trans *)
 lemma cpx_frees_conf_lfpx: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
-                           â\88\80L2. L1 ⦻*[cpx h G, cfull, f1] L2 →
+                           â\88\80L2. 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
@@ -56,8 +37,8 @@ lemma cpx_frees_conf_lfpx: ∀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
@@ -131,8 +112,8 @@ lemma cpx_frees_conf_lfpx: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
     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=3 by lsubf_refl, lsubf_beta, sor_inv_sle_dx, sle_inv_tl_sn/ ] -HgT2
-    #gT0 #HgT0 #HgT20
+    [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 (⫱gT0)) /3 width=3 by frees_fwd_isfin, isfin_tl/ -H #g2 #Hg2 #_
     @(ex2_intro … g2)
@@ -159,17 +140,17 @@ lemma cpx_frees_conf_lfpx: ∀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-.
 
-(* Basic_2A1: was: cpx_frees_trans *)
+(* Basic_2A1: uses: 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-.
 
-(* Basic_2A1: was: lpx_frees_trans *)
+(* Basic_2A1: uses: 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-.