X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fground_2%2Fstar.ma;h=18f028acc6eda865266c5937b79e1a6b393d7d72;hb=b33a11c031f1519628b0f90dc20df7e0507d5723;hp=c183111ddf429584bd0aca1b6548a9ae9ceee1cd;hpb=a8c166f1e1baeeae04553058bd179420ada8bbe7;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/ground_2/star.ma b/matita/matita/contribs/lambda_delta/ground_2/star.ma
index c183111dd..18f028acc 100644
--- a/matita/matita/contribs/lambda_delta/ground_2/star.ma
+++ b/matita/matita/contribs/lambda_delta/ground_2/star.ma
@@ -18,7 +18,7 @@ include "ground_2/notation.ma".
 
 (* PROPERTIES OF RELATIONS **************************************************)
 
-definition Decidable: Prop → Prop ≝ λR. R ∨ (R → False).
+definition Decidable: Prop → Prop ≝ λR. R ∨ (R → ⊥).
 
 definition confluent2: ∀A. ∀R1,R2: relation A. Prop ≝ λA,R1,R2.
                        ∀a0,a1. R1 a0 a1 → ∀a2. R2 a0 a2 →
@@ -99,10 +99,10 @@ lemma TC_transitive2: ∀A,R1,R2.
 qed.
 
 definition NF: ∀A. relation A → relation A → predicate A ≝
-   λA,R,S,a1. ∀a2. R a1 a2 → S a1 a2.
+   λA,R,S,a1. ∀a2. R a1 a2 → S a2 a1.
 
 inductive SN (A) (R,S:relation A): predicate A ≝
-| SN_intro: ∀a1. (∀a2. R a1 a2 → (S a1 a2 → False) → SN A R S a2) → SN A R S a1
+| SN_intro: ∀a1. (∀a2. R a1 a2 → (S a2 a1 → ⊥) → SN A R S a2) → SN A R S a1
 .
 
 lemma NF_to_SN: ∀A,R,S,a. NF A R S a → SN A R S a.
@@ -110,3 +110,16 @@ lemma NF_to_SN: ∀A,R,S,a. NF A R S a → SN A R S a.
 @SN_intro #a2 #HRa12 #HSa12
 elim (HSa12 ?) -HSa12 /2 width=1/
 qed.
+
+definition NF_sn: ∀A. relation A → relation A → predicate A ≝
+   λA,R,S,a2. ∀a1. R a1 a2 → S a2 a1.
+
+inductive SN_sn (A) (R,S:relation A): predicate A ≝
+| SN_sn_intro: ∀a2. (∀a1. R a1 a2 → (S a2 a1 → ⊥) → SN_sn A R S a1) → SN_sn A R S a2
+.
+
+lemma NF_to_SN_sn: ∀A,R,S,a. NF_sn A R S a → SN_sn A R S a.
+#A #R #S #a2 #Ha2
+@SN_sn_intro #a1 #HRa12 #HSa12
+elim (HSa12 ?) -HSa12 /2 width=1/
+qed.