- more commutations with superclosure: fpb_lfdeq

[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 26289760bd6072eddb473062f455c647cd2a6419..56ce310164b3b7157a50c3260057f3988c01e112 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
@@ -36,16 +36,18 @@ theorem lfxs_flat: ∀R,I,L1,L2,V,T.
 /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
+theorem lfxs_conf: ∀R1,R2.
+                   lexs_frees_confluent R1 cfull →
+                   lexs_frees_confluent R2 cfull →
+                   R_confluent2_lfxs R1 R2 R1 R2 →
+                   ∀T. confluent2 … (lfxs R1 T) (lfxs R2 T).
+#R1 #R2 #HR1 #HR2 #HR12 #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
+  elim (HR1 … Hf … HL01) -HL01 #f1 #Hf1 #H1
+  elim (HR2 … 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/
@@ -53,6 +55,6 @@ elim (lexs_conf … HL01 … HL02) /2 width=3 by ex2_intro/ [ | -HL01 -HL02 ]
   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/
+  elim (HR12 … HV01 … HV02 K1 … K2) /2 width=3 by ex2_intro/
 ]
 qed-.