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

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn.ma
index fddde2de5bdd33df53e458ea82a49f0ca7172eba..eb640da891b1a9f7b97b3a91db504b5d8da0820c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn.ma
@@ -16,16 +16,16 @@ include "basic_2/grammar/lenv_length.ma".
 
 (* SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS *********)
 
-inductive lpx_sn (R:lenv→relation term): relation lenv ≝
+inductive lpx_sn (R:relation4 bind2 lenv term term): relation lenv ≝
 | lpx_sn_atom: lpx_sn R (⋆) (⋆)
 | lpx_sn_pair: ∀I,K1,K2,V1,V2.
-               lpx_sn R K1 K2 → R K1 V1 V2 →
-               lpx_sn R (K1. ⓑ{I} V1) (K2. ⓑ{I} V2)
+               lpx_sn R K1 K2 → R I K1 V1 V2 →
+               lpx_sn R (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
 .
 
 (* Basic properties *********************************************************)
 
-lemma lpx_sn_refl: ∀R. (∀L. reflexive ? (R L)) → reflexive … (lpx_sn R).
+lemma lpx_sn_refl: ∀R. (∀I,L. reflexive ? (R I L)) → reflexive … (lpx_sn R).
 #R #HR #L elim L -L /2 width=1 by lpx_sn_atom, lpx_sn_pair/
 qed-.
 
@@ -41,16 +41,16 @@ qed-.
 lemma lpx_sn_inv_atom1: ∀R,L2. lpx_sn R (⋆) L2 → L2 = ⋆.
 /2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
 
-fact lpx_sn_inv_pair1_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K1,V1. L1 = K1. ⓑ{I} V1 →
-                           ∃∃K2,V2. lpx_sn R K1 K2 & R K1 V1 V2 & L2 = K2. ⓑ{I} V2.
+fact lpx_sn_inv_pair1_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K1,V1. L1 = K1.ⓑ{I}V1 →
+                           ∃∃K2,V2. lpx_sn R K1 K2 & R I K1 V1 V2 & L2 = K2.ⓑ{I}V2.
 #R #L1 #L2 * -L1 -L2
 [ #J #K1 #V1 #H destruct
 | #I #K1 #K2 #V1 #V2 #HK12 #HV12 #J #L #W #H destruct /2 width=5 by ex3_2_intro/
 ]
 qed-.
 
-lemma lpx_sn_inv_pair1: ∀R,I,K1,V1,L2. lpx_sn R (K1. ⓑ{I} V1) L2 →
-                        ∃∃K2,V2. lpx_sn R K1 K2 & R K1 V1 V2 & L2 = K2. ⓑ{I} V2.
+lemma lpx_sn_inv_pair1: ∀R,I,K1,V1,L2. lpx_sn R (K1.ⓑ{I}V1) L2 →
+                        ∃∃K2,V2. lpx_sn R K1 K2 & R I K1 V1 V2 & L2 = K2.ⓑ{I}V2.
 /2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
 
 fact lpx_sn_inv_atom2_aux: ∀R,L1,L2. lpx_sn R L1 L2 → L2 = ⋆ → L1 = ⋆.
@@ -63,21 +63,21 @@ qed-.
 lemma lpx_sn_inv_atom2: ∀R,L1. lpx_sn R L1 (⋆) → L1 = ⋆.
 /2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
 
-fact lpx_sn_inv_pair2_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K2,V2. L2 = K2. ⓑ{I} V2 →
-                           ∃∃K1,V1. lpx_sn R K1 K2 & R K1 V1 V2 & L1 = K1. ⓑ{I} V1.
+fact lpx_sn_inv_pair2_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K2,V2. L2 = K2.ⓑ{I}V2 →
+                           ∃∃K1,V1. lpx_sn R K1 K2 & R I K1 V1 V2 & L1 = K1.ⓑ{I}V1.
 #R #L1 #L2 * -L1 -L2
 [ #J #K2 #V2 #H destruct
 | #I #K1 #K2 #V1 #V2 #HK12 #HV12 #J #K #W #H destruct /2 width=5 by ex3_2_intro/
 ]
 qed-.
 
-lemma lpx_sn_inv_pair2: ∀R,I,L1,K2,V2. lpx_sn R L1 (K2. ⓑ{I} V2) →
-                        ∃∃K1,V1. lpx_sn R K1 K2 & R K1 V1 V2 & L1 = K1. ⓑ{I} V1.
+lemma lpx_sn_inv_pair2: ∀R,I,L1,K2,V2. lpx_sn R L1 (K2.ⓑ{I}V2) →
+                        ∃∃K1,V1. lpx_sn R K1 K2 & R I K1 V1 V2 & L1 = K1.ⓑ{I}V1.
 /2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
 
 lemma lpx_sn_inv_pair: ∀R,I1,I2,L1,L2,V1,V2.
                        lpx_sn R (L1.ⓑ{I1}V1) (L2.ⓑ{I2}V2) →
-                       ∧∧ lpx_sn R L1 L2 & R L1 V1 V2 & I1 = I2.
+                       ∧∧ lpx_sn R L1 L2 & R I1 L1 V1 V2 & I1 = I2.
 #R #I1 #I2 #L1 #L2 #V1 #V2 #H elim (lpx_sn_inv_pair1 … H) -H
 #L0 #V0 #HL10 #HV10 #H destruct /2 width=1 by and3_intro/
 qed-.