update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / sex_tc.ma

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 c892868cbbff68842c0366b806b05d385339ae94..379cfc75146fdc8ff995e03bd8024a131e71cad9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
@@ -18,7 +18,7 @@ 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.
-                                 â\88\80f. ð\9d\90\88â¦\83fâ¦\84 → s_rs_transitive … RP (λ_.sex RN RP f).
+                                 â\88\80f. ð\9d\90\88â\9dªfâ\9d« → s_rs_transitive … RP (λ_.sex RN RP f).
 
 (* Properties with transitive closure ***************************************)
 
@@ -28,28 +28,28 @@ lemma sex_tc_refl: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
 
 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}).
+                      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}).
+                      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.
@@ -68,21 +68,21 @@ 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 →
-                        â\88\80f,L1,L. L1 ⪤[RN,RP,f] L â\86\92 ð\9d\90\88â¦\83fâ¦\84 →
+                        â\88\80f,L1,L. L1 ⪤[RN,RP,f] L â\86\92 ð\9d\90\88â\9dªfâ\9d« →
                         ∀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 // ]
@@ -99,7 +99,7 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma sex_tc_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
-                 â\88\80f. ð\9d\90\88â¦\83fâ¦\84 → ∀L1,L2. TC … (sex RN RP f) L1 L2 → L1 ⪤[RN,CTC … RP,f] L2.
+                 â\88\80f. ð\9d\90\88â\9dªfâ\9d« → ∀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.