update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
index 8fddc58967479ca39416bd6778be5ab544949dc5..f2ab35f91a30c403f9948b99c2956341e66b7e08 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs.ma
@@ -14,7 +14,7 @@
 
 include "ground_2/relocation/rtmap_id.ma".
 include "basic_2/notation/relations/relationstar_4.ma".
-include "basic_2/syntax/lenv_ext2.ma".
+include "basic_2/syntax/cext2.ma".
 include "basic_2/relocation/lexs.ma".
 include "basic_2/static/frees.ma".
 
@@ -26,17 +26,6 @@ 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_frees_confluent: predicate (relation3 …) ≝
-                              λRN.
-                              ∀f1,L,T1. L ⊢ 𝐅*⦃T1⦄ ≡ f1 → ∀T2. RN L T1 T2 →
-                              ∃∃f2. L ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ f1.
-
-definition lexs_frees_confluent: relation (relation3 …) ≝
-                                 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.
@@ -44,6 +33,16 @@ definition R_confluent2_lfxs: relation4 (relation3 lenv term term)
                               ∀L1. L0 ⪤*[RP1, T0] L1 → ∀L2. L0 ⪤*[RP2, T0] L2 →
                               ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
 
+definition lfxs_confluent: relation … ≝
+                           λR1,R2. 
+                           ∀K1,K,V1. K1 ⪤*[R1, V1] K → ∀V. R1 K1 V1 V →
+                           ∀K2. K ⪤*[R2, V] K2 → K ⪤*[R2, V1] K2.
+
+definition lfxs_transitive: relation3 ? (relation3 ?? term) … ≝
+                            λR1,R2,R3.
+                            ∀K1,K,V1. K1 ⪤*[R1, V1] K →
+                            ∀V. R1 K1 V1 V → ∀V2. R2 K V V2 → R3 K1 V1 V2.
+
 (* Basic inversion lemmas ***************************************************)
 
 lemma lfxs_inv_atom_sn: ∀R,Y2,T. ⋆ ⪤*[R, T] Y2 → Y2 = ⋆.
@@ -294,13 +293,6 @@ lemma lfxs_bind_repl_dx: ∀R,I,I1,L1,L2,T.
 /3 width=5 by lexs_pair_repl, ex2_intro/
 qed-.
 
-lemma lfxs_sym: ∀R. lexs_frees_confluent (cext2 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
-/5 width=5 by sle_lexs_trans, lexs_sym, cext2_sym, ex2_intro/
-qed-.
-
 (* Basic_2A1: uses: llpx_sn_co *)
 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.