X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Frelocation%2Fsex_tc.ma;h=0a95ed3b0f5720832af36230e9b3f61c57061157;hb=98e786e1a6bd7b621e37ba7cd4098d4a0a6f8278;hp=8d1cf55389dfd0df2135d685a5fe8ee1a18138c9;hpb=5b5dca0c118dfbe3ba8f0514ef07549544eb7810;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
index 8d1cf5538..0a95ed3b0 100644
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
@@ -12,13 +12,13 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/lib/star.ma".
+include "ground/lib/star.ma".
 include "static_2/relocation/sex.ma".
 
 (* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****)
 
 definition s_rs_transitive_isid: relation (relation3 lenv bind bind) ≝ λRN,RP.
-                                 ∀f. 𝐈⦃f⦄ → s_rs_transitive … RP (λ_.sex RN RP f).
+                                 ∀f. 𝐈❪f❫ → s_rs_transitive … RP (λ_.sex RN RP f).
 
 (* Properties with transitive closure ***************************************)
 
@@ -27,29 +27,29 @@ lemma sex_tc_refl: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
 /3 width=1 by sex_refl, TC_reflexive/ qed.
 
 lemma sex_tc_next_sn: ∀RN,RP. c_reflexive … RN →
-                      ∀f,I2,L1,L2. TC … (sex RN RP f) L1 L2 → ∀I1. RN L1 I1 I2 → 
-                      TC … (sex RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                      ∀f,I2,L1,L2. TC … (sex RN RP f) L1 L2 → ∀I1. RN L1 I1 I2 →
+                      TC … (sex RN RP (↑f)) (L1.ⓘ[I1]) (L2.ⓘ[I2]).
 #RN #RP #HRN #f #I2 #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
 /3 width=3 by sex_next, TC_strap, inj/
 qed.
 
 lemma sex_tc_next_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
                       ∀f,I1,I2,L1. (CTC … RN) L1 I1 I2 → ∀L2. L1 ⪤[RN,RP,f] L2 →
-                      TC … (sex RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                      TC … (sex RN RP (↑f)) (L1.ⓘ[I1]) (L2.ⓘ[I2]).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by sex_refl, sex_next, step, inj/
 qed.
 
 lemma sex_tc_push_sn: ∀RN,RP. c_reflexive … RP →
-                      ∀f,I2,L1,L2. TC … (sex RN RP f) L1 L2 → ∀I1. RP L1 I1 I2 → 
-                      TC … (sex RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                      ∀f,I2,L1,L2. TC … (sex RN RP f) L1 L2 → ∀I1. RP L1 I1 I2 →
+                      TC … (sex RN RP (⫯f)) (L1.ⓘ[I1]) (L2.ⓘ[I2]).
 #RN #RP #HRP #f #I2 #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
 /3 width=3 by sex_push, TC_strap, inj/
 qed.
 
 lemma sex_tc_push_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
                       ∀f,I1,I2,L1. (CTC … RP) L1 I1 I2 → ∀L2. L1 ⪤[RN,RP,f] L2 →
-                      TC … (sex RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                      TC … (sex RN RP (⫯f)) (L1.ⓘ[I1]) (L2.ⓘ[I2]).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by sex_refl, sex_push, step, inj/
 qed.
@@ -68,27 +68,27 @@ qed.
 
 theorem sex_tc_next: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
                      ∀f,I1,I2,L1. (CTC … RN) L1 I1 I2 → ∀L2. TC … (sex RN RP f) L1 L2 →
-                     TC … (sex RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                     TC … (sex RN RP (↑f)) (L1.ⓘ[I1]) (L2.ⓘ[I2]).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by sex_tc_next_sn, sex_tc_refl, trans_TC/
 qed.
 
 theorem sex_tc_push: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
                      ∀f,I1,I2,L1. (CTC … RP) L1 I1 I2 → ∀L2. TC … (sex RN RP f) L1 L2 →
-                     TC … (sex RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                     TC … (sex RN RP (⫯f)) (L1.ⓘ[I1]) (L2.ⓘ[I2]).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by sex_tc_push_sn, sex_tc_refl, trans_TC/
 qed.
 
 (* Basic_2A1: uses: TC_lpx_sn_ind *)
 theorem sex_tc_step_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
-                        ∀f,L1,L. L1 ⪤[RN,RP,f] L → 𝐈⦃f⦄ →
+                        ∀f,L1,L. L1 ⪤[RN,RP,f] L → 𝐈❪f❫ →
                         ∀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 >(sex_inv_atom1 … H) -Y // ]
 #f #I1 #I #L1 #L #HL1 #HI1 #IH #Hf #Y #H
-[ elim (isid_inv_next … Hf) -Hf //
-| lapply (isid_inv_push … Hf ??) -Hf [3: |*: // ] #Hf
+[ elim (pr_isi_inv_next … Hf) -Hf //
+| lapply (pr_isi_inv_push … Hf ??) -Hf [3: |*: // ] #Hf
   elim (sex_inv_push1 … H) -H #I2 #L2 #HL2 #HI2 #H destruct
   @sex_push [ /2 width=1 by/ ] -L2 -IH
   @(TC_strap … HI1) -HI1
@@ -99,7 +99,7 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma sex_tc_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
-                 ∀f. 𝐈⦃f⦄ → ∀L1,L2. TC … (sex RN RP f) L1 L2 → L1 ⪤[RN,CTC … RP,f] L2.
+                 ∀f. 𝐈❪f❫ → ∀L1,L2. TC … (sex 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 sex_tc_step_dx, sex_tc_inj_dx/
 qed.