notational change for lexs

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lexs_lexs.ma

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 91dc222975f7defbd3a3995f8d0cf5649cf49023..c8edf5e5347c33e0696882ead30fc32b40b2f236 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma
@@ -13,8 +13,6 @@
 (**************************************************************************)
 
 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 *****)
@@ -24,9 +22,9 @@ include "basic_2/relocation/drops.ma".
 theorem lexs_trans_gen (RN1) (RP1) (RN2) (RP2) (RN) (RP) (f):
                        lexs_transitive RN1 RN2 RN RN1 RP1 →
                        lexs_transitive RP1 RP2 RP RN1 RP1 →
-                       â\88\80L1,L0. L1 ⦻*[RN1, RP1, f] L0 →
-                       â\88\80L2. L0 ⦻*[RN2, RP2, f] L2 →
-                       L1 ⦻*[RN, RP, f] L2.
+                       â\88\80L1,L0. L1 ⪤*[RN1, RP1, f] L0 →
+                       â\88\80L2. L0 ⪤*[RN2, RP2, f] L2 →
+                       L1 ⪤*[RN, RP, f] L2.
 #RN1 #RP1 #RN2 #RP2 #RN #RP #f #HN #HP #L1 #L0 #H elim H -f -L1 -L0
 [ #f #L2 #H >(lexs_inv_atom1 … H) -L2 //
 | #f #I #K1 #K #V1 #V #HK1 #HV1 #IH #L2 #H elim (lexs_inv_next1 … H) -H
@@ -45,8 +43,8 @@ theorem lexs_trans (RN) (RP) (f): lexs_transitive RN RN RN RN RP →
 (* Basic_2A1: includes: lpx_sn_conf *)
 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) →
+                  (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ⫯g = ⫱*[n] f → R_pw_confluent2_lexs RN1 RN2 RN1 RP1 RN2 RP2 g K V) →
+                  (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ↑g = ⫱*[n] f → R_pw_confluent2_lexs 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
@@ -76,9 +74,9 @@ theorem lexs_canc_dx: ∀RN,RP,f. Transitive … (lexs RN RP f) →
 /3 width=3 by/ qed-.
 
 lemma lexs_meet: ∀RN,RP,L1,L2.
-                 â\88\80f1. L1 ⦻*[RN, RP, f1] L2 →
-                 â\88\80f2. L1 ⦻*[RN, RP, f2] L2 →
-                 â\88\80f. f1 â\8b\92 f2 â\89¡ f â\86\92 L1 ⦻*[RN, RP, f] L2.
+                 â\88\80f1. L1 ⪤*[RN, RP, f1] L2 →
+                 â\88\80f2. L1 ⪤*[RN, RP, f2] L2 →
+                 â\88\80f. f1 â\8b\92 f2 â\89¡ f â\86\92 L1 ⪤*[RN, RP, f] L2.
 #RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 //
 #f1 #I #L1 #L2 #V1 #V2 #_ #HV12 #IH #f2 #H #f #Hf
 elim (pn_split f2) * #g2 #H2 destruct
@@ -89,9 +87,9 @@ try elim (lexs_inv_push … H) try elim (lexs_inv_next … H) -H
 qed-.
 
 lemma lexs_join: ∀RN,RP,L1,L2.
-                 â\88\80f1. L1 ⦻*[RN, RP, f1] L2 →
-                 â\88\80f2. L1 ⦻*[RN, RP, f2] L2 →
-                 â\88\80f. f1 â\8b\93 f2 â\89¡ f â\86\92 L1 ⦻*[RN, RP, f] L2.
+                 â\88\80f1. L1 ⪤*[RN, RP, f1] L2 →
+                 â\88\80f2. L1 ⪤*[RN, RP, f2] L2 →
+                 â\88\80f. f1 â\8b\93 f2 â\89¡ f â\86\92 L1 ⪤*[RN, RP, f] L2.
 #RN #RP #L1 #L2 #f1 #H elim H -f1 -L1 -L2 //
 #f1 #I #L1 #L2 #V1 #V2 #_ #HV12 #IH #f2 #H #f #Hf
 elim (pn_split f2) * #g2 #H2 destruct