- the relation for pointwise extensions now takes a binder as argument

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lpx_sn_lpx_sn.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn_lpx_sn.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn_lpx_sn.ma
index 3cd97e96d891e6ad9605118f18f1247aeb62c6a9..bd72cf61eefab1627272aa860f72c648a70283b1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn_lpx_sn.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn_lpx_sn.ma
@@ -16,33 +16,33 @@ include "basic_2/relocation/lpx_sn.ma".
 
 (* SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS *********)
 
-definition lpx_sn_confluent: relation (lenv→relation term) ≝ λR1,R2.
+definition lpx_sn_confluent: relation (relation3 lenv term term) ≝ λR1,R2.
                              ∀L0,T0,T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
-                             ∀L1. lpx_sn R1 L0 L1 → ∀L2. lpx_sn R2 L0 L2 →
+                             ∀L1. lpx_sn (λ_.R1) L0 L1 → ∀L2. lpx_sn (λ_.R2) L0 L2 →
                              ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
 
-definition lpx_sn_transitive: relation (lenv→relation term) ≝ λR1,R2.
-                              ∀L1,T1,T. R1 L1 T1 T → ∀L2. lpx_sn R1 L1 L2 →
+definition lpx_sn_transitive: relation (relation3 lenv term term) ≝ λR1,R2.
+                              ∀L1,T1,T. R1 L1 T1 T → ∀L2. lpx_sn (λ_.R1) L1 L2 →
                               ∀T2. R2 L2 T T2 → R1 L1 T1 T2.
 
 (* Main properties **********************************************************)
 
-theorem lpx_sn_trans: ∀R. lpx_sn_transitive R R → Transitive … (lpx_sn R).
+theorem lpx_sn_trans: ∀R. lpx_sn_transitive R R → Transitive … (lpx_sn (λ_.R)).
 #R #HR #L1 #L #H elim H -L1 -L //
 #I #L1 #L #V1 #V #HL1 #HV1 #IHL1 #X #H
-elim (lpx_sn_inv_pair1 … H) -H #L2 #V2 #HL2 #HV2 #H destruct /3 width=5/
+elim (lpx_sn_inv_pair1 … H) -H #L2 #V2 #HL2 #HV2 #H destruct /3 width=5 by lpx_sn_pair/
 qed-.
 
 theorem lpx_sn_conf: ∀R1,R2. lpx_sn_confluent R1 R2 →
-                     confluent2 … (lpx_sn R1) (lpx_sn R2).
+                     confluent2 … (lpx_sn (λ_.R1)) (lpx_sn (λ_.R2)).
 #R1 #R2 #HR12 #L0 @(f_ind … length … L0) -L0 #n #IH *
 [ #_ #X1 #H1 #X2 #H2 -n
   >(lpx_sn_inv_atom1 … H1) -X1
-  >(lpx_sn_inv_atom1 … H2) -X2 /2 width=3/
+  >(lpx_sn_inv_atom1 … H2) -X2 /2 width=3 by lpx_sn_atom, ex2_intro/
 | #L0 #I #V0 #Hn #X1 #H1 #X2 #H2 destruct
   elim (lpx_sn_inv_pair1 … H1) -H1 #L1 #V1 #HL01 #HV01 #H destruct
   elim (lpx_sn_inv_pair1 … H2) -H2 #L2 #V2 #HL02 #HV02 #H destruct
   elim (IH … HL01 … HL02) -IH normalize // #L #HL1 #HL2
-  elim (HR12 … HV01 … HV02 … HL01 … HL02) -L0 -V0 /3 width=5/
+  elim (HR12 … HV01 … HV02 … HL01 … HL02) -L0 -V0 /3 width=5 by lpx_sn_pair, ex2_intro/
 ]
 qed-.