improved lexs_conf, now holds under weaker hypotheses ...

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma
index 3a779a649182b05ca4917e1aa643e21f6ec2c6c4..d0dbc756838768eaac6d596985ab1b287ad7dee3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma
@@ -32,12 +32,14 @@ inductive lexs (RN,RP:relation3 lenv term term): rtmap → relation lenv ≝
 interpretation "generic entrywise extension (local environment)"
    'RelationStar RN RP f L1 L2 = (lexs RN RP f L1 L2).
 
-definition lexs_confluent: relation6 (relation3 lenv term term)
-                                     (relation3 lenv term term) … ≝
-                           λR1,R2,RN1,RP1,RN2,RP2.
-                           ∀f,L0,T0,T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
-                           ∀L1. L0 ⦻*[RN1, RP1, f] L1 → ∀L2. L0 ⦻*[RN2, RP2, f] L2 →
-                           ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
+definition lexs_pw_confluent2_R: relation3 lenv term term → relation3 lenv term term →
+                                 relation3 lenv term term → relation3 lenv term term →
+                                 relation3 lenv term term → relation3 lenv term term →
+                                 relation3 rtmap lenv term ≝
+                                 λR1,R2,RN1,RP1,RN2,RP2,f,L0,T0.
+                                 ∀T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
+                                 ∀L1. L0 ⦻*[RN1, RP1, f] L1 → ∀L2. L0 ⦻*[RN2, RP2, f] L2 →
+                                 ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
 
 definition lexs_transitive: relation5 (relation3 lenv term term)
                                       (relation3 lenv term term) … ≝

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma
index 7e7c3debca3fefda7eb09d60ef299918e5fa23fa..91dc222975f7defbd3a3995f8d0cf5649cf49023 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma
@@ -15,6 +15,7 @@
 include "ground_2/relocation/rtmap_sand.ma".
 include "ground_2/relocation/rtmap_sor.ma".
 include "basic_2/relocation/lexs.ma".
+include "basic_2/relocation/drops.ma".
 
 (* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****)
 
@@ -42,27 +43,24 @@ theorem lexs_trans (RN) (RP) (f): lexs_transitive RN RN RN RN RP →
 /2 width=9 by lexs_trans_gen/ qed-.
 
 (* Basic_2A1: includes: lpx_sn_conf *)
-theorem lexs_conf (RN1) (RP1) (RN2) (RP2): lexs_confluent RN1 RN2 RN1 RP1 RN2 RP2 →
-                                           lexs_confluent RP1 RP2 RN1 RP1 RN2 RP2 →
-                                           ∀f. confluent2 … (lexs RN1 RP1 f) (lexs RN2 RP2 f).
-#RN1 #RP1 #RN2 #RP2 #HRN #HRP #f #L0
-generalize in match f; -f elim L0 -L0
-[ #f #L1 #HL01 #L2 #HL02 -HRN -HRP
-  lapply (lexs_inv_atom1 … HL01) -HL01 #H destruct
-  lapply (lexs_inv_atom1 … HL02) -HL02 #H destruct
-  /2 width=3 by ex2_intro/
-| #K0 #I #V0 #IH #f #L1 #HL01 #L2 #HL02
-  elim (pn_split f) * #g #H destruct
-  [ elim (lexs_inv_push1 … HL01) -HL01 #K1 #V1 #HK01 #HV01 #H destruct
-    elim (lexs_inv_push1 … HL02) -HL02 #K2 #V2 #HK02 #HV02 #H destruct
-    elim (IH … HK01 … HK02) -IH #K #HK1 #HK2
-    elim (HRP … HV01 … HV02 … HK01 … HK02) -HRP -HRN -K0 -V0
-    /3 width=5 by lexs_push, ex2_intro/
-  | elim (lexs_inv_next1 … HL01) -HL01 #K1 #V1 #HK01 #HV01 #H destruct
-    elim (lexs_inv_next1 … HL02) -HL02 #K2 #V2 #HK02 #HV02 #H destruct
-    elim (IH … HK01 … HK02) -IH #K #HK1 #HK2
-    elim (HRN … HV01 … HV02 … HK01 … HK02) -HRN -HRP -K0 -V0
-    /3 width=5 by lexs_next, ex2_intro/
+theorem lexs_conf (RN1) (RP1) (RN2) (RP2):
+                  ∀L,f.
+                  (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V →  ⫱*[n] f = ⫯g → lexs_pw_confluent2_R RN1 RN2 RN1 RP1 RN2 RP2 g K V) →
+                  (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V →  ⫱*[n] f = ↑g → lexs_pw_confluent2_R RP1 RP2 RN1 RP1 RN2 RP2 g K V) →
+                  pw_confluent2 … (lexs RN1 RP1 f) (lexs RN2 RP2 f) L.
+#RN1 #RP1 #RN2 #RP2 #L elim L -L
+[ #f #_ #_ #L1 #H1 #L2 #H2 >(lexs_inv_atom1 … H1) >(lexs_inv_atom1 … H2) -H2 -H1
+  /2 width=3 by lexs_atom, ex2_intro/
+| #L #I #V #IH #f elim (pn_split f) * #g #H destruct
+  #HN #HP #Y1 #H1 #Y2 #H2
+  [ elim (lexs_inv_push1 … H1) -H1 #L1 #V1 #HL1 #HV1 #H destruct
+    elim (lexs_inv_push1 … H2) -H2 #L2 #V2 #HL2 #HV2 #H destruct
+    elim (HP … 0 … HV1 … HV2 … HL1 … HL2) -HV1 -HV2 /2 width=2 by drops_refl/ #V #HV1 #HV2
+    elim (IH … HL1 … HL2) -IH -HL1 -HL2 /3 width=5 by drops_drop, lexs_push, ex2_intro/
+  | elim (lexs_inv_next1 … H1) -H1 #L1 #V1 #HL1 #HV1 #H destruct
+    elim (lexs_inv_next1 … H2) -H2 #L2 #V2 #HL2 #HV2 #H destruct
+    elim (HN … 0 … HV1 … HV2 … HL1 … HL2) -HV1 -HV2 /2 width=2 by drops_refl/ #V #HV1 #HV2
+    elim (IH … HL1 … HL2) -IH -HL1 -HL2 /3 width=5 by drops_drop, lexs_next, ex2_intro/
   ]
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/star.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/star.ma
index 8849d759beeaf774379ecc33015d548353b6e913..b0e3e6be601368d027e964864d73c371eb1bb8d3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/star.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/star.ma
@@ -34,9 +34,12 @@ definition left_cancellable: ∀A. ∀R: relation A. Prop ≝ λA,R.
 definition right_cancellable: ∀A. ∀R: relation A. Prop ≝ λA,R.
                               ∀a1,a0. R a1 a0 → ∀a2. R a2 a0 → R a1 a2.
 
-definition confluent2: ∀A. ∀R1,R2: relation A. Prop ≝ λA,R1,R2.
-                       ∀a0,a1. R1 a0 a1 → ∀a2. R2 a0 a2 →
-                       ∃∃a. R2 a1 a & R1 a2 a.
+definition pw_confluent2: ∀A. relation A → relation A → predicate A ≝ λA,R1,R2,a0.
+                          ∀a1. R1 a0 a1 → ∀a2. R2 a0 a2 →
+                          ∃∃a. R2 a1 a & R1 a2 a.
+
+definition confluent2: ∀A. relation (relation A) ≝ λA,R1,R2.
+                       ∀a0. pw_confluent2 A R1 R2 a0.
 
 definition transitive2: ∀A. ∀R1,R2: relation A. Prop ≝ λA,R1,R2.
                         ∀a1,a0. R1 a1 a0 → ∀a2. R2 a0 a2 →