X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs_lfxs.ma;h=95b89cd809e2cbca53835b2fe0ae071c9a93768b;hb=98fbba1b68d457807c73ebf70eb2a48696381da4;hp=8f92b0f34a563ca823116421df719089266fdec8;hpb=65e6209e0758832835ba8d14304a1548d059a634;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
index 8f92b0f34..95b89cd80 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
@@ -13,8 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/relocation/lexs_lexs.ma".
-include "basic_2/static/frees_fqup.ma".
-include "basic_2/static/frees_frees.ma".
+include "basic_2/static/frees_drops.ma".
 include "basic_2/static/lfxs.ma".
 
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
@@ -22,7 +21,7 @@ include "basic_2/static/lfxs.ma".
 (* Advanced properties ******************************************************)
 
 lemma lfxs_inv_frees: ∀R,L1,L2,T. L1 ⪤*[R, T] L2 →
-                      ∀f. L1 ⊢ 𝐅*⦃T⦄ ≡ f → L1 ⪤*[R, cfull, f] L2.
+                      ∀f. L1 ⊢ 𝐅*⦃T⦄ ≡ f → L1 ⪤*[cext2 R, cfull, f] L2.
 #R #L1 #L2 #T * /3 width=6 by frees_mono, lexs_eq_repl_back/
 qed-.
 
@@ -31,12 +30,12 @@ lemma lfxs_dec: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) →
                 ∀L1,L2,T. Decidable (L1 ⪤*[R, T] L2).
 #R #HR #L1 #L2 #T
 elim (frees_total L1 T) #f #Hf
-elim (lexs_dec R cfull HR … L1 L2 f)
-/4 width=3 by lfxs_inv_frees, cfull_dec, ex2_intro, or_intror, or_introl/
+elim (lexs_dec (cext2 R) cfull … L1 L2 f)
+/4 width=3 by lfxs_inv_frees, cfull_dec, ext2_dec, ex2_intro, or_intror, or_introl/
 qed-.
 
 lemma lfxs_pair_sn_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
-                          lexs_frees_confluent … R1 cfull →
+                          lexs_frees_confluent … (cext2 R1) cfull →
                           ∀L1,L2,V. L1 ⪤*[R1, V] L2 → ∀I,T.
                           ∃∃L. L1 ⪤*[R1, ②{I}V.T] L & L ⪤*[R2, V] L2.
 #R1 #R2 #HR1 #HR2 #HR #L1 #L2 #V * #f #Hf #HL12 * [ #p ] #I #T
@@ -48,14 +47,14 @@ lemma lfxs_pair_sn_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. refl
 lapply(frees_mono … H … Hf) -H #H1
 lapply (sor_eq_repl_back1 … Hy … H1) -y1 #Hy
 lapply (sor_inv_sle_sn … Hy) -y2 #Hfg
-elim (lexs_sle_split … HR1 HR2 … HL12 … Hfg) -HL12 #L #HL1 #HL2
+elim (lexs_sle_split (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #L #HL1 #HL2
 lapply (sle_lexs_trans … HL1 … Hfg) // #H
 elim (HR … Hf … H) -HR -Hf -H
 /4 width=7 by sle_lexs_trans, ex2_intro/
 qed-.
 
 lemma lfxs_flat_dx_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
-                          lexs_frees_confluent … R1 cfull →
+                          lexs_frees_confluent … (cext2 R1) cfull →
                           ∀L1,L2,T. L1 ⪤*[R1, T] L2 → ∀I,V.
                           ∃∃L. L1 ⪤*[R1, ⓕ{I}V.T] L & L ⪤*[R2, T] L2.
 #R1 #R2 #HR1 #HR2 #HR #L1 #L2 #T * #f #Hf #HL12 #I #V
@@ -64,14 +63,14 @@ elim (frees_inv_flat … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2
 lapply (sor_eq_repl_back2 … Hy … H2) -y2 #Hy
 lapply (sor_inv_sle_dx … Hy) -y1 #Hfg
-elim (lexs_sle_split … HR1 HR2 … HL12 … Hfg) -HL12 #L #HL1 #HL2
+elim (lexs_sle_split (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #L #HL1 #HL2
 lapply (sle_lexs_trans … HL1 … Hfg) // #H
 elim (HR … Hf … H) -HR -Hf -H
 /4 width=7 by sle_lexs_trans, ex2_intro/
 qed-.
 
 lemma lfxs_bind_dx_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
-                          lexs_frees_confluent … R1 cfull →
+                          lexs_frees_confluent … (cext2 R1) cfull →
                           ∀I,L1,L2,V1,T. L1.ⓑ{I}V1 ⪤*[R1, T] L2 → ∀p.
                           ∃∃L,V. L1 ⪤*[R1, ⓑ{p,I}V1.T] L & L.ⓑ{I}V ⪤*[R2, T] L2 & R1 L1 V1 V.
 #R1 #R2 #HR1 #HR2 #HR #I #L1 #L2 #V1 #T * #f #Hf #HL12 #p
@@ -82,9 +81,10 @@ lapply (tl_eq_repl … H2) -H2 #H2
 lapply (sor_eq_repl_back2 … Hy … H2) -y2 #Hy
 lapply (sor_inv_sle_dx … Hy) -y1 #Hfg
 lapply (sle_inv_tl_sn … Hfg) -Hfg #Hfg
-elim (lexs_sle_split … HR1 HR2 … HL12 … Hfg) -HL12 #Y #H #HL2
+elim (lexs_sle_split (cext2 R1) (cext2 R2) … HL12 … Hfg) -HL12 /2 width=1 by ext2_refl/ #Y #H #HL2
 lapply (sle_lexs_trans … H … Hfg) // #H0
-elim (lexs_inv_next1 … H) -H #L #V #HL1 #HV0 #H destruct
+elim (lexs_inv_next1 … H) -H #Z #L #HL1 #H
+elim (ext2_inv_pair_sn … H) -H #V #HV #H1 #H2 destruct
 elim (HR … Hf … H0) -HR -Hf -H0
 /4 width=7 by sle_lexs_trans, ex3_2_intro, ex2_intro/
 qed-.
@@ -96,7 +96,7 @@ theorem lfxs_bind: ∀R,p,I,L1,L2,V1,V2,T.
                    L1 ⪤*[R, V1] L2 → L1.ⓑ{I}V1 ⪤*[R, T] L2.ⓑ{I}V2 →
                    L1 ⪤*[R, ⓑ{p,I}V1.T] L2.
 #R #p #I #L1 #L2 #V1 #V2 #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
-elim (lexs_fwd_pair … Hf2) -Hf2 #Hf2 #_ elim (sor_isfin_ex f1 (⫱f2))
+lapply (lexs_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫱f2))
 /3 width=7 by frees_fwd_isfin, frees_bind, lexs_join, isfin_tl, ex2_intro/
 qed.
 
@@ -108,9 +108,17 @@ theorem lfxs_flat: ∀R,I,L1,L2,V,T.
 /3 width=7 by frees_fwd_isfin, frees_flat, lexs_join, ex2_intro/
 qed.
 
+theorem lfxs_bind_void: ∀R,p,I,L1,L2,V,T.
+                        L1 ⪤*[R, V] L2 → L1.ⓧ ⪤*[R, T] L2.ⓧ →
+                        L1 ⪤*[R, ⓑ{p,I}V.T] L2.
+#R #p #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
+lapply (lexs_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫱f2))
+/3 width=7 by frees_fwd_isfin, frees_bind_void, lexs_join, isfin_tl, ex2_intro/
+qed.
+
 theorem lfxs_conf: ∀R1,R2.
-                   lexs_frees_confluent R1 cfull →
-                   lexs_frees_confluent R2 cfull →
+                   lexs_frees_confluent (cext2 R1) cfull →
+                   lexs_frees_confluent (cext2 R2) cfull →
                    R_confluent2_lfxs R1 R2 R1 R2 →
                    ∀T. confluent2 … (lfxs R1 T) (lfxs R2 T).
 #R1 #R2 #HR1 #HR2 #HR12 #T #L0 #L1 * #f1 #Hf1 #HL01 #L2 * #f #Hf #HL02
@@ -123,11 +131,17 @@ elim (lexs_conf … HL01 … HL02) /2 width=3 by ex2_intro/ [ | -HL01 -HL02 ]
   lapply (sle_lexs_trans … HL1 … H1) // -HL1 -H1 #HL1
   lapply (sle_lexs_trans … HL2 … H2) // -HL2 -H2 #HL2
   /3 width=5 by ex2_intro/
-| #g #I #K0 #V0 #n #HLK0 #Hgf #V1 #HV01 #V2 #HV02 #K1 #HK01 #K2 #HK02
-  elim (frees_drops_next … Hf … HLK0 … Hgf) -Hf -HLK0 -Hgf #g0 #Hg0 #H0
-  lapply (sle_lexs_trans … HK01 … H0) // -HK01 #HK01
-  lapply (sle_lexs_trans … HK02 … H0) // -HK02 #HK02
-  elim (HR12 … HV01 … HV02 K1 … K2) /2 width=3 by ex2_intro/
+| #g * #I0 [2: #V0 ] #K0 #n #HLK0 #Hgf #Z1 #H1 #Z2 #H2 #K1 #HK01 #K2 #HK02
+  [ elim (ext2_inv_pair_sn … H1) -H1 #V1 #HV01 #H destruct
+    elim (ext2_inv_pair_sn … H2) -H2 #V2 #HV02 #H destruct
+    elim (frees_inv_drops_next … Hf … HLK0 … Hgf) -Hf -HLK0 -Hgf #g0 #Hg0 #H0
+    lapply (sle_lexs_trans … HK01 … H0) // -HK01 #HK01
+    lapply (sle_lexs_trans … HK02 … H0) // -HK02 #HK02
+    elim (HR12 … HV01 … HV02 K1 … K2) /3 width=3 by ext2_pair, ex2_intro/
+  | lapply (ext2_inv_unit_sn … H1) -H1 #H destruct
+    lapply (ext2_inv_unit_sn … H2) -H2 #H destruct
+    /3 width=3 by ext2_unit, ex2_intro/
+  ]
 ]
 qed-.
 
@@ -148,3 +162,10 @@ lemma lfnxs_inv_flat: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) →
 #R #HR #I #L1 #L2 #V #T #H elim (lfxs_dec … HR L1 L2 V)
 /4 width=1 by lfxs_flat, or_intror, or_introl/
 qed-.
+
+lemma lfnxs_inv_bind_void: ∀R. (∀L,T1,T2. Decidable (R L T1 T2)) →
+                           ∀p,I,L1,L2,V,T. (L1 ⪤*[R, ⓑ{p,I}V.T] L2 → ⊥) →
+                           (L1 ⪤*[R, V] L2 → ⊥) ∨ (L1.ⓧ ⪤*[R, T] L2.ⓧ → ⊥).
+#R #HR #p #I #L1 #L2 #V #T #H elim (lfxs_dec … HR L1 L2 V)
+/4 width=2 by lfxs_bind_void, or_intror, or_introl/
+qed-.