X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs.ma;h=a1d50e69f243bd9c9ea175138630e9d3008e16df;hb=56dd0e9f60e0dabfb587b014755fd4dad27960bb;hp=dba35a74a47133e5e02215421dc13a2d6cc3f44d;hpb=075441b55fa8a6fa693a1c96ed60ab4d87c42a2d;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
index dba35a74a..a1d50e69f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
@@ -14,7 +14,6 @@
 
 include "ground_2/relocation/rtmap_id.ma".
 include "basic_2/notation/relations/relationstar_4.ma".
-include "basic_2/grammar/ceq.ma".
 include "basic_2/relocation/lexs.ma".
 include "basic_2/static/frees.ma".
 
@@ -26,14 +25,25 @@ definition lfxs (R) (T): relation lenv ≝
 interpretation "generic extension on referred entries (local environment)"
    'RelationStar R T L1 L2 = (lfxs R T L1 L2).
 
-definition R_confluent_lfxs: relation4 (relation3 lenv term term)
-                                       (relation3 lenv term term) … ≝
-                             λR1,R2,RP1,RP2.
-                             ∀L0,T0,T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
-                             ∀L1. L0 ⦻*[RP1, T0] L1 → ∀L2. L0 ⦻*[RP2, T0] L2 →
-                             ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
+definition R_frees_confluent: predicate (relation3 lenv term term) ≝
+                              λRN.
+                              ∀f1,L,T1. L ⊢ 𝐅*⦃T1⦄ ≡ f1 → ∀T2. RN L T1 T2 →
+                              ∃∃f2. L ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ f1.
 
-(* Basic properties ***********************************************************)
+definition lexs_frees_confluent: relation (relation3 lenv term term) ≝
+                                 λRN,RP.
+                                 ∀f1,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f1 →
+                                 ∀L2. L1 ⦻*[RN, RP, f1] L2 →
+                                 ∃∃f2. L2 ⊢ 𝐅*⦃T⦄ ≡ f2 & f2 ⊆ f1.
+
+definition R_confluent2_lfxs: relation4 (relation3 lenv term term)
+                                        (relation3 lenv term term) … ≝
+                              λR1,R2,RP1,RP2.
+                              ∀L0,T0,T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
+                              ∀L1. L0 ⦻*[RP1, T0] L1 → ∀L2. L0 ⦻*[RP2, T0] L2 →
+                              ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
+
+(* Basic properties *********************************************************)
 
 lemma lfxs_atom: ∀R,I. ⋆ ⦻*[R, ⓪{I}] ⋆.
 /3 width=3 by lexs_atom, frees_atom, ex2_intro/
@@ -67,15 +77,18 @@ lemma lfxs_pair_repl_dx: ∀R,I,L1,L2,T,V,V1.
 /3 width=5 by lexs_pair_repl, ex2_intro/
 qed-.
 
+lemma lfxs_sym: ∀R. lexs_frees_confluent R cfull →
+                (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
+                ∀T. symmetric … (lfxs R T).
+#R #H1R #H2R #T #L1 #L2 * #f1 #Hf1 #HL12 elim (H1R … Hf1 … HL12) -Hf1
+/4 width=5 by sle_lexs_trans, lexs_sym, ex2_intro/
+qed-.
+
 lemma lfxs_co: ∀R1,R2. (∀L,T1,T2. R1 L T1 T2 → R2 L T1 T2) →
                ∀L1,L2,T. L1 ⦻*[R1, T] L2 → L1 ⦻*[R2, T] L2.
 #R1 #R2 #HR #L1 #L2 #T * /4 width=7 by lexs_co, ex2_intro/
 qed-.
 
-lemma pippo: ∀R1,R2,RP1,RP2. R_confluent_lfxs R1 R2 RP1 RP2 →
-             lexs_confluent R1 R2 RP1 cfull RP2 cfull.
-#R1 #R2 #RP1 #RP2 #HR #f #L0 #T0 #T1 #HT01 #T2 #HT02 #L1 #HL01 #L2 #HL02  
-
 (* Basic inversion lemmas ***************************************************)
 
 lemma lfxs_inv_atom_sn: ∀R,I,Y2. ⋆ ⦻*[R, ⓪{I}] Y2 → Y2 = ⋆.
@@ -87,7 +100,7 @@ lemma lfxs_inv_atom_dx: ∀R,I,Y1. Y1 ⦻*[R, ⓪{I}] ⋆ → Y1 = ⋆.
 qed-.
 
 lemma lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⦻*[R, ⋆s] Y2 →
-                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
                      ∃∃I,L1,L2,V1,V2. L1 ⦻*[R, ⋆s] L2 &
                                       Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 #R * [ | #Y1 #I #V1 ] #Y2 #s * #f #H1 #H2
@@ -100,7 +113,7 @@ lemma lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⦻*[R, ⋆s] Y2 →
 qed-.
 
 lemma lfxs_inv_zero: ∀R,Y1,Y2. Y1 ⦻*[R, #0] Y2 →
-                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
                      ∃∃I,L1,L2,V1,V2. L1 ⦻*[R, V1] L2 & R L1 V1 V2 &
                                       Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 #R #Y1 #Y2 * #f #H1 #H2 elim (frees_inv_zero … H1) -H1 *
@@ -111,7 +124,7 @@ lemma lfxs_inv_zero: ∀R,Y1,Y2. Y1 ⦻*[R, #0] Y2 →
 qed-.
 
 lemma lfxs_inv_lref: ∀R,Y1,Y2,i. Y1 ⦻*[R, #⫯i] Y2 →
-                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
+                     (Y1 = ⋆ ∧ Y2 = ⋆) ∨
                      ∃∃I,L1,L2,V1,V2. L1 ⦻*[R, #i] L2 &
                                       Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 #R #Y1 #Y2 #i * #f #H1 #H2 elim (frees_inv_lref … H1) -H1 *