X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flexs_tc.ma;h=09536b034075f95ce2f8913d9b0de7bda7860ad9;hb=75f395f0febd02de8e0f881d918a8812b1425c8d;hp=70cfdbd7156e52ac88b9a31459a4e84b9d1e71ed;hpb=d59f344b1e4b377e2f06abd9f8856d686d21b222;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_tc.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_tc.ma
index 70cfdbd71..09536b034 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_tc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_tc.ma
@@ -34,7 +34,7 @@ lemma lexs_tc_next_sn: ∀RN,RP. c_reflexive … RN →
 qed.
 
 lemma lexs_tc_next_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                       ∀f,I1,I2,L1. (LTC … RN) L1 I1 I2 → ∀L2. L1 ⪤*[RN, RP, f] L2 →
+                       ∀f,I1,I2,L1. (CTC … RN) L1 I1 I2 → ∀L2. L1 ⪤*[RN, RP, f] L2 →
                        TC … (lexs RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by lexs_refl, lexs_next, step, inj/
@@ -48,18 +48,18 @@ lemma lexs_tc_push_sn: ∀RN,RP. c_reflexive … RP →
 qed.
 
 lemma lexs_tc_push_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                       ∀f,I1,I2,L1. (LTC … RP) L1 I1 I2 → ∀L2. L1 ⪤*[RN, RP, f] L2 →
+                       ∀f,I1,I2,L1. (CTC … RP) L1 I1 I2 → ∀L2. L1 ⪤*[RN, RP, f] L2 →
                        TC … (lexs RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by lexs_refl, lexs_push, step, inj/
 qed.
 
-lemma lexs_tc_inj_sn: ∀RN,RP,f,L1,L2. L1 ⪤*[RN, RP, f] L2 → L1 ⪤*[LTC … RN, RP, f] L2.
+lemma lexs_tc_inj_sn: ∀RN,RP,f,L1,L2. L1 ⪤*[RN, RP, f] L2 → L1 ⪤*[CTC … RN, RP, f] L2.
 #RN #RP #f #L1 #L2 #H elim H -f -L1 -L2
 /3 width=1 by lexs_push, lexs_next, inj/
 qed.
 
-lemma lexs_tc_inj_dx: ∀RN,RP,f,L1,L2. L1 ⪤*[RN, RP, f] L2 → L1 ⪤*[RN, LTC … RP, f] L2.
+lemma lexs_tc_inj_dx: ∀RN,RP,f,L1,L2. L1 ⪤*[RN, RP, f] L2 → L1 ⪤*[RN, CTC … RP, f] L2.
 #RN #RP #f #L1 #L2 #H elim H -f -L1 -L2
 /3 width=1 by lexs_push, lexs_next, inj/
 qed.
@@ -67,14 +67,14 @@ qed.
 (* Main properties with transitive closure **********************************)
 
 theorem lexs_tc_next: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                      ∀f,I1,I2,L1. (LTC … RN) L1 I1 I2 → ∀L2. TC … (lexs RN RP f) L1 L2 →
+                      ∀f,I1,I2,L1. (CTC … RN) L1 I1 I2 → ∀L2. TC … (lexs RN RP f) L1 L2 →
                       TC … (lexs RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by lexs_tc_next_sn, lexs_tc_refl, trans_TC/
 qed.
 
 theorem lexs_tc_push: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                      ∀f,I1,I2,L1. (LTC … RP) L1 I1 I2 → ∀L2. TC … (lexs RN RP f) L1 L2 →
+                      ∀f,I1,I2,L1. (CTC … RP) L1 I1 I2 → ∀L2. TC … (lexs RN RP f) L1 L2 →
                       TC … (lexs RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by lexs_tc_push_sn, lexs_tc_refl, trans_TC/
@@ -83,7 +83,7 @@ qed.
 (* Basic_2A1: uses: TC_lpx_sn_ind *)
 theorem lexs_tc_step_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
                          ∀f,L1,L. L1 ⪤*[RN, RP, f] L → 𝐈⦃f⦄ →
-                         ∀L2. L ⪤*[RN, LTC … RP, f] L2 → L1⪤* [RN, LTC … RP, f] L2.
+                         ∀L2. L ⪤*[RN, CTC … RP, f] L2 → L1⪤* [RN, CTC … RP, f] L2.
 #RN #RP #HRP #f #L1 #L #H elim H -f -L1 -L
 [ #f #_ #Y #H -HRP >(lexs_inv_atom1 … H) -Y // ]
 #f #I1 #I #L1 #L #HL1 #HI1 #IH #Hf #Y #H
@@ -99,7 +99,7 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma lexs_tc_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
-                  ∀f. 𝐈⦃f⦄ → ∀L1,L2. TC … (lexs RN RP f) L1 L2 → L1 ⪤*[RN, LTC … RP, f] L2.
+                  ∀f. 𝐈⦃f⦄ → ∀L1,L2. TC … (lexs RN RP f) L1 L2 → L1 ⪤*[RN, CTC … RP, f] L2.
 #RN #RP #HRP #f #Hf #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
 /3 width=3 by lexs_tc_step_dx, lexs_tc_inj_dx/
 qed.
@@ -107,13 +107,13 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 lemma lexs_inv_tc_sn: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                      ∀f,L1,L2. L1 ⪤*[LTC … RN, RP, f] L2 → TC … (lexs RN RP f) L1 L2.
+                      ∀f,L1,L2. L1 ⪤*[CTC … RN, RP, f] L2 → TC … (lexs RN RP f) L1 L2.
 #RN #RP #HRN #HRP #f #L1 #L2 #H elim H -f -L1 -L2
 /2 width=1 by lexs_tc_next, lexs_tc_push_sn, lexs_atom, inj/
 qed-.
 
 lemma lexs_inv_tc_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                      ∀f,L1,L2. L1 ⪤*[RN, LTC … RP, f] L2 → TC … (lexs RN RP f) L1 L2.
+                      ∀f,L1,L2. L1 ⪤*[RN, CTC … RP, f] L2 → TC … (lexs RN RP f) L1 L2.
 #RN #RP #HRN #HRP #f #L1 #L2 #H elim H -f -L1 -L2
 /2 width=1 by lexs_tc_push, lexs_tc_next_sn, lexs_atom, inj/
 qed-.