advances towards confluence of reduction in local environments ...

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

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 5360aeddc29fd9c35a25b545716b0056d119ff98..26289760bd6072eddb473062f455c647cd2a6419 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
@@ -13,6 +13,8 @@
 (**************************************************************************)
 
 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/lfxs.ma".
 
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
@@ -33,3 +35,24 @@ theorem lfxs_flat: ∀R,I,L1,L2,V,T.
 #R #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2 elim (sor_isfin_ex f1 f2)
 /3 width=7 by frees_fwd_isfin, frees_flat, lexs_join, ex2_intro/
 qed.
+
+theorem lfxs_conf: ∀R. lexs_frees_confluent R cfull →
+                   R_confluent2_lfxs R R R R →
+                   ∀T. confluent … (lfxs R T).
+#R #H1R #H2R #T #L0 #L1 * #f1 #Hf1 #HL01 #L2 * #f #Hf #HL02
+lapply (frees_mono … Hf1 … Hf) -Hf1 #Hf12
+lapply (lexs_eq_repl_back … HL01 … Hf12) -f1 #HL01
+elim (lexs_conf … HL01 … HL02) /2 width=3 by ex2_intro/ [ | -HL01 -HL02 ]
+[ #L #HL1 #HL2
+  elim (H1R … Hf … HL01) -HL01 #f1 #Hf1 #H1
+  elim (H1R … Hf … HL02) -HL02 #f2 #Hf2 #H2
+  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 (H2R … HV01 … HV02 K1 … K2) /2 width=3 by ex2_intro/
+]
+qed-.