milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / lib / functions.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/functions.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/functions.ma
index 64fbae2e12f8ab025271d282715e22af1765ea09..739fb8d4f47cbc12fe91ddcf06b9bfd694b2f4a0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/functions.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/functions.ma
@@ -16,6 +16,19 @@ include "ground_2/lib/relations.ma".
 
 (* FUNCTIONS ****************************************************************)
 
-definition left_identity (A:Type[0]) (f): predicate A ≝ λi. ∀a:A. a = f i a.
+definition left_identity (A) (f): predicate A ≝ λi. ∀a:A. a = f i a.
 
-definition right_identity (A:Type[0]) (f): predicate A ≝ λi. ∀a:A. a = f a i.
+definition right_identity (A) (f): predicate A ≝ λi. ∀a:A. a = f a i.
+
+definition compatible_2 (A) (B):
+                        relation3 … (relation A) (relation B) ≝
+                        λf,Sa,Sb.
+                        ∀a1,a2. Sa a1 a2 → Sb (f a1) (f a2).
+
+definition compatible_3 (A) (B) (C):
+                        relation4 … (relation A) (relation B) (relation C) ≝
+                        λf,Sa,Sb,Sc.
+                        ∀a1,a2. Sa a1 a2 → ∀b1,b2. Sb b1 b2 → Sc (f a1 b1) (f a2 b2).
+
+definition annulment_2 (A) (f): predicate A ≝
+                       λi:A. ∀a1,a2. i = f a1 a2 → ∧∧ i = a1 & i = a2.