previous lemma proved ...

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lexs.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lexs.ma
index d55d50dbbdf06e67958a5ec62c50028f9b0e220e..a192a206ecddcbabbb2093b499d68ac037090404 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lexs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lexs.ma
@@ -152,3 +152,11 @@ elim (lexs_liftable_co_dedropable … H1RN H1RP H2RN H2RP … HLK1 … HK12 …
 #X #HX #HLK2 #H1L12 elim (lexs_inv_push1 … HX) -HX
 #L2 #V2 #H2L12 #HV12 #H destruct /2 width=6 by ex4_2_intro/
 qed-.
+
+lemma drops_atom2_lexs_conf: ∀RN,RP,b,f1,L1. ⬇*[b, f1] L1 ≡ ⋆ → 𝐔⦃f1⦄ →
+                             ∀f,L2. L1 ⦻*[RN, RP, f] L2 →
+                             ∀f2. f1 ~⊚ f2 ≡f → ⬇*[b, f1] L2 ≡ ⋆.
+#RN #RP #b #f1 #L1 #H1 #Hf1 #f #L2 #H2 #f2 #H3
+elim (lexs_co_dropable_sn … H1 … H2 … H3) // -H1 -H2 -H3 -Hf1
+#L #H #HL2 lapply (lexs_inv_atom1 … H) -H //
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lstar.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lstar.ma
index f4734a9b0e7b741d300e37e1288ad1ffac3c36ff..8badfaf9d469fa5112e31b721d4c4ad91e358786 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lstar.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lstar.ma
@@ -14,7 +14,6 @@
 
 include "ground_2/lib/lstar.ma".
 include "basic_2/relocation/lreq_lreq.ma".
-include "basic_2/relocation/drops.ma".
 
 (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
 

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 c786518ee0a5b9844c6f921bba8281f60e280844..250760ca73c42e83ab6ff87be3e3fc978848bd32 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".
@@ -23,19 +22,6 @@ 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 →
@@ -56,8 +42,8 @@ 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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma
index c5762eacbbe202d8c246ec8f26d0bb63782efc5f..f153ad53cab0704ed87278833552481d6705f9ff 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma
@@ -14,6 +14,7 @@
 
 include "ground_2/relocation/nstream_coafter.ma".
 include "basic_2/relocation/drops_drops.ma".
+include "basic_2/static/frees_fqup.ma".
 include "basic_2/static/frees_frees.ma".
 
 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
@@ -153,61 +154,26 @@ lemma frees_fwd_coafter: ∀b,f2,L,U. L ⊢ 𝐅*⦃U⦄ ≡ f2 →
 
 (* Inversion lemmas with generic slicing for local environments *************)
 
+lemma frees_inv_lifts_ex: ∀b,f2,L,U. L ⊢ 𝐅*⦃U⦄ ≡ f2 →
+                          ∀f,K. ⬇*[b, f] L ≡ K → ∀T. ⬆*[f] T ≡ U →
+                          ∃∃f1. f ~⊚ f1 ≡ f2 & K ⊢ 𝐅*⦃T⦄ ≡ f1.
+#b #f2 #L #U #Hf2 #f #K #HLK #T elim (frees_total K T)
+/3 width=9 by frees_fwd_coafter, ex2_intro/
+qed-.
+
+lemma 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.
+#b #f #L #U #H #K #HLK #T #HTU elim(frees_inv_lifts_ex … H … HLK … HTU) -b -L -U
+#f1 #Hf #Hf1 elim (coafter_inv_nxx … Hf) -Hf
+/3 width=5 by frees_eq_repl_back, coafter_isid_inv_sn/
+qed-.
+
 lemma frees_inv_lifts: ∀b,f2,L,U. L ⊢ 𝐅*⦃U⦄ ≡ f2 →
                        ∀f,K. ⬇*[b, f] L ≡ K → ∀T. ⬆*[f] T ≡ U →
                        ∀f1. f ~⊚ f1 ≡ f2 → K ⊢ 𝐅*⦃T⦄ ≡ f1.
-#b #f2 #L #U #H lapply (frees_fwd_isfin … H) elim H -f2 -L -U
-[ #f2 #I #Hf2 #_ #f #K #H1 #T #H2 #f1 #H3
-  lapply (coafter_fwd_isid2 … H3 … Hf2) -H3 // -Hf2 #Hf1
-  elim (drops_inv_atom1 … H1) -H1 #H #_ destruct
-  elim (lifts_inv_atom2 … H2) -H2 * /2 width=3 by frees_atom/
-| #f2 #I #L #W #s #_ #IH #Hf2 #f #Y #H1 #T #H2 #f1 #H3
-  lapply (isfin_fwd_push … Hf2 ??) -Hf2 [3: |*: // ] #Hf2
-  lapply (lifts_inv_sort2 … H2) -H2 #H destruct
-  elim (coafter_inv_xxp … H3) -H3 [1,3: * |*: // ]
-  [ #g #g1 #Hf2 #H #H0 destruct
-    elim (drops_inv_skip1 … H1) -H1 #K #V #HLK #_ #H destruct
-  | #g #Hf2 #H destruct
-    lapply (drops_inv_drop1 … H1) -H1
-  ] /3 width=4 by frees_sort/
-| #f2 #I #L #W #_ #IH #Hf2 #f #Y #H1 #T #H2 #f1 #H3
-  lapply (isfin_inv_next … Hf2 ??) -Hf2 [3: |*: // ] #Hf2
-  elim (lifts_inv_lref2 … H2) -H2 #i #H2 #H destruct
-  lapply (at_inv_xxp … H2 ?) -H2 // * #g #H #H0 destruct
-  elim (drops_inv_skip1 … H1) -H1 #K #V #HLK #HVW #H destruct
-  elim (coafter_inv_pxn … H3) -H3 [ |*: // ] #g1 #Hf2 #H destruct
-  /3 width=4 by frees_zero/
-| #f2 #I #L #W #j #_ #IH #Hf2 #f #Y #H1 #T #H2 #f1 #H3
-  lapply (isfin_fwd_push … Hf2 ??) -Hf2 [3: |*: // ] #Hf2
-  elim (lifts_inv_lref2 … H2) -H2 #x #H2 #H destruct
-  elim (coafter_inv_xxp … H3) -H3 [1,3: * |*: // ]
-  [ #g #g1 #Hf2 #H #H0 destruct
-    elim (drops_inv_skip1 … H1) -H1 #K #V #HLK #HVW #H destruct
-    elim (at_inv_xpn … H2) -H2 [ |*: // ] #j #Hg #H destruct
-  | #g #Hf2 #H destruct
-    lapply (drops_inv_drop1 … H1) -H1
-    lapply (at_inv_xnn … H2 ????) -H2 [5: |*: // ]
-  ] /4 width=4 by lifts_lref, frees_lref/
-| #f2 #I #L #W #l #_ #IH #Hf2 #f #Y #H1 #T #H2 #f1 #H3
-  lapply (isfin_fwd_push … Hf2 ??) -Hf2 [3: |*: // ] #Hf2
-  lapply (lifts_inv_gref2 … H2) -H2 #H destruct
-  elim (coafter_inv_xxp … H3) -H3 [1,3: * |*: // ]
-  [ #g #g1 #Hf2 #H #H0 destruct
-    elim (drops_inv_skip1 … H1) -H1 #K #V #HLK #_ #H destruct
-  | #g #Hf2 #H destruct
-    lapply (drops_inv_drop1 … H1) -H1
-  ] /3 width=4 by frees_gref/
-| #f2W #f2U #f2 #p #I #L #W #U #_ #_ #H1f2 #IHW #IHU #H2f2 #f #K #H1 #X #H2 #f1 #H3
-  elim (sor_inv_isfin3 … H1f2) // #H1f2W #H
-  lapply (isfin_inv_tl … H) -H
-  elim (lifts_inv_bind2 … H2) -H2 #V #T #HVW #HTU #H destruct
-  elim (coafter_inv_sor … H3 … H1f2) -H3 -H1f2 // #f1W #f1U #H2f2W #H
-  elim (coafter_inv_tl0 … H) -H /4 width=5 by frees_bind, drops_skip/
-| #f2W #f2U #f2 #I #L #W #U #_ #_ #H1f2 #IHW #IHU #H2f2 #f #K #H1 #X #H2 #f1 #H3
-  elim (sor_inv_isfin3 … H1f2) //
-  elim (lifts_inv_flat2 … H2) -H2 #V #T #HVW #HTU #H destruct
-  elim (coafter_inv_sor … H3 … H1f2) -H3 -H1f2 /3 width=5 by frees_flat/
-]
+#b #f2 #L #U #H #f #K #HLK #T #HTU #f1 #Hf2 elim (frees_inv_lifts_ex … H … HLK … HTU) -b -L -U
+/3 width=7 by frees_eq_repl_back, coafter_inj/
 qed-.
 
 lemma frees_inv_drops: ∀f2,L,U. L ⊢ 𝐅*⦃U⦄ ≡ f2 →

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
index f43eb4e95956f239b843d1aa744e5a955455bff0..0a3f287bb168a152e26e85cf0a546b2b6b270ee7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
@@ -14,7 +14,6 @@
 
 include "basic_2/relocation/drops_ceq.ma".
 include "basic_2/relocation/drops_lexs.ma".
-include "basic_2/static/frees_fqup.ma".
 include "basic_2/static/frees_drops.ma".
 include "basic_2/static/lfxs.ma".
 

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_coafter.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_coafter.ma
index 56449d8385412e88314dc4f7add69c3cc2986a86..c6e4b3a960368be5384b66f1f5d6695ac42d7039 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_coafter.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_coafter.ma
@@ -326,14 +326,15 @@ lemma coafter_isid_inv_sn: ∀f1,f2,f. f1 ~⊚ f2 ≡ f → 𝐈⦃f1⦄ → f2
 lemma coafter_isid_inv_dx: ∀f1,f2,f. f1 ~⊚ f2 ≡ f → 𝐈⦃f2⦄ → 𝐈⦃f⦄.
 /4 width=4 by eq_id_isid, coafter_isid_dx, coafter_mono/ qed-.
 
-(* Properties with uniform relocations **************************************)
+(* Properties with test for uniform relocations *****************************)
 
-lemma coafter_uni_sn: ∀i,f. 𝐔❴i❵ ~⊚ f ≡ ↑*[i] f.
-#i elim i -i /2 width=5 by coafter_isid_sn, coafter_next/
+lemma coafter_isuni_isid: ∀f2. 𝐈⦃f2⦄ → ∀f1. 𝐔⦃f1⦄ → f1 ~⊚ f2 ≡ f2.
+#f #Hf #g #H elim H -g
+/3 width=5 by coafter_isid_sn, coafter_eq_repl_back0, coafter_next, eq_push_inv_isid/
 qed.
-(*
-(* Properties on isuni ******************************************************)
 
+
+(*
 lemma coafter_isid_isuni: ∀f1,f2. 𝐈⦃f2⦄ → 𝐔⦃f1⦄ → f1 ~⊚ ⫯f2 ≡ ⫯f1.
 #f1 #f2 #Hf2 #H elim H -H
 /5 width=7 by coafter_isid_dx, coafter_eq_repl_back2, coafter_next, coafter_push, eq_push_inv_isid/
@@ -349,9 +350,15 @@ lemma coafter_uni_next2: ∀f2. 𝐔⦃f2⦄ → ∀f1,f. ⫯f2 ~⊚ f1 ≡ f 
   /3 width=5 by coafter_next/
 ]
 qed.
+*)
 
-(* Properties on uni ********************************************************)
+(* Properties with uniform relocations **************************************)
+
+lemma coafter_uni_sn: ∀i,f. 𝐔❴i❵ ~⊚ f ≡ ↑*[i] f.
+#i elim i -i /2 width=5 by coafter_isid_sn, coafter_next/
+qed.
 
+(*
 lemma coafter_uni: ∀n1,n2. 𝐔❴n1❵ ~⊚ 𝐔❴n2❵ ≡ 𝐔❴n1+n2❵.
 @nat_elim2
 /4 width=5 by coafter_uni_next2, coafter_isid_sn, coafter_isid_dx, coafter_next/
@@ -360,7 +367,7 @@ qed.
 (* Forward lemmas on at *****************************************************)
 
 lemma coafter_at_fwd: ∀i,i1,f. @⦃i1, f⦄ ≡ i → ∀f2,f1. f2 ~⊚ f1 ≡ f →
-                    ∃∃i2. @⦃i1, f1⦄ ≡ i2 & @⦃i2, f2⦄ ≡ i.
+                      ∃∃i2. @⦃i1, f1⦄ ≡ i2 & @⦃i2, f2⦄ ≡ i.
 #i elim i -i [2: #i #IH ] #i1 #f #Hf #f2 #f1 #Hf21
 [ elim (at_inv_xxn … Hf) -Hf [1,3:* |*: // ]
   [1: #g #j1 #Hg #H0 #H |2,4: #g #Hg #H ]
@@ -377,7 +384,7 @@ lemma coafter_at_fwd: ∀i,i1,f. @⦃i1, f⦄ ≡ i → ∀f2,f1. f2 ~⊚ f1 ≡
 qed-.
 
 lemma coafter_fwd_at: ∀i,i2,i1,f1,f2. @⦃i1, f1⦄ ≡ i2 → @⦃i2, f2⦄ ≡ i →
-                    ∀f. f2 ~⊚ f1 ≡ f → @⦃i1, f⦄ ≡ i.
+                      ∀f. f2 ~⊚ f1 ≡ f → @⦃i1, f⦄ ≡ i.
 #i elim i -i [2: #i #IH ] #i2 #i1 #f1 #f2 #Hf1 #Hf2 #f #Hf
 [ elim (at_inv_xxn … Hf2) -Hf2 [1,3: * |*: // ]
   #g2 [ #j2 ] #Hg2 [ #H22 ] #H20
@@ -395,13 +402,13 @@ lemma coafter_fwd_at: ∀i,i2,i1,f1,f2. @⦃i1, f1⦄ ≡ i2 → @⦃i2, f2⦄ 
 qed-.
 
 lemma coafter_fwd_at2: ∀f,i1,i. @⦃i1, f⦄ ≡ i → ∀f1,i2. @⦃i1, f1⦄ ≡ i2 →
-                     ∀f2. f2 ~⊚ f1 ≡ f → @⦃i2, f2⦄ ≡ i.
+                       ∀f2. f2 ~⊚ f1 ≡ f → @⦃i2, f2⦄ ≡ i.
 #f #i1 #i #Hf #f1 #i2 #Hf1 #f2 #H elim (coafter_at_fwd … Hf … H) -f
 #j1 #H #Hf2 <(at_mono … Hf1 … H) -i1 -i2 //
 qed-.
 
 lemma coafter_fwd_at1: ∀i,i2,i1,f,f2. @⦃i1, f⦄ ≡ i → @⦃i2, f2⦄ ≡ i →
-                     ∀f1. f2 ~⊚ f1 ≡ f → @⦃i1, f1⦄ ≡ i2.
+                       ∀f1. f2 ~⊚ f1 ≡ f → @⦃i1, f1⦄ ≡ i2.
 #i elim i -i [2: #i #IH ] #i2 #i1 #f #f2 #Hf #Hf2 #f1 #Hf1
 [ elim (at_inv_xxn … Hf) -Hf [1,3: * |*: // ]
   #g [ #j1 ] #Hg [ #H01 ] #H00
@@ -421,7 +428,7 @@ qed-.
 (* Properties with at *******************************************************)
 
 lemma coafter_uni_dx: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 →
-                    ∀f. f2 ~⊚ 𝐔❴i1❵ ≡ f → 𝐔❴i2❵ ~⊚ ⫱*[i2] f2 ≡ f.
+                      ∀f. f2 ~⊚ 𝐔❴i1❵ ≡ f → 𝐔❴i2❵ ~⊚ ⫱*[i2] f2 ≡ f.
 #i2 elim i2 -i2
 [ #i1 #f2 #Hf2 #f #Hf
   elim (at_inv_xxp … Hf2) -Hf2 // #g2 #H1 #H2 destruct
@@ -440,7 +447,7 @@ lemma coafter_uni_dx: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 →
 qed.
 
 lemma coafter_uni_sn: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 →
-                    ∀f. 𝐔❴i2❵ ~⊚ ⫱*[i2] f2 ≡ f → f2 ~⊚ 𝐔❴i1❵ ≡ f.
+                      ∀f. 𝐔❴i2❵ ~⊚ ⫱*[i2] f2 ≡ f → f2 ~⊚ 𝐔❴i1❵ ≡ f.
 #i2 elim i2 -i2
 [ #i1 #f2 #Hf2 #f #Hf
   elim (at_inv_xxp … Hf2) -Hf2 // #g2 #H1 #H2 destruct
@@ -456,7 +463,7 @@ lemma coafter_uni_sn: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 →
 qed-.
 
 lemma coafter_uni_succ_dx: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 →
-                         ∀f. f2 ~⊚ 𝐔❴⫯i1❵ ≡ f → 𝐔❴⫯i2❵ ~⊚ ⫱*[⫯i2] f2 ≡ f.
+                           ∀f. f2 ~⊚ 𝐔❴⫯i1❵ ≡ f → 𝐔❴⫯i2❵ ~⊚ ⫱*[⫯i2] f2 ≡ f.
 #i2 elim i2 -i2
 [ #i1 #f2 #Hf2 #f #Hf
   elim (at_inv_xxp … Hf2) -Hf2 // #g2 #H1 #H2 destruct
@@ -476,7 +483,7 @@ lemma coafter_uni_succ_dx: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 →
 qed.
 
 lemma coafter_uni_succ_sn: ∀i2,i1,f2. @⦃i1, f2⦄ ≡ i2 →
-                         ∀f. 𝐔❴⫯i2❵ ~⊚ ⫱*[⫯i2] f2 ≡ f → f2 ~⊚ 𝐔❴⫯i1❵ ≡ f.
+                           ∀f. 𝐔❴⫯i2❵ ~⊚ ⫱*[⫯i2] f2 ≡ f → f2 ~⊚ 𝐔❴⫯i1❵ ≡ f.
 #i2 elim i2 -i2
 [ #i1 #f2 #Hf2 #f #Hf
   elim (at_inv_xxp … Hf2) -Hf2 // #g2 #H1 #H2 destruct