setoids.ma split into setoids.ma + setoids1.ma

[helm.git] / helm / software / matita / nlibrary / logic / connectives.ma

diff --git a/helm/software/matita/nlibrary/logic/connectives.ma b/helm/software/matita/nlibrary/logic/connectives.ma
index 6eb2375dcc895b3b8e4e6068572345382f349e34..026e9216951c9224737b6493953317effd635369 100644 (file)
--- a/helm/software/matita/nlibrary/logic/connectives.ma
+++ b/helm/software/matita/nlibrary/logic/connectives.ma
@@ -18,9 +18,6 @@ ninductive True: CProp ≝
   I : True.
 
 ninductive False: CProp ≝.
-(* elimination principle *)
-ndefinition False_rect ≝ λP: False → Type.λp: False.
- match p in False return λp. P p with [].
 
 ndefinition Not: CProp → CProp ≝
   λA. A → False.
@@ -42,3 +39,18 @@ ninductive Ex (A:Type) (P:A → CProp) : CProp ≝
     ex_intro: ∀x:A. P x → Ex A P.
 
 interpretation "exists" 'exists x = (Ex ? x).
+
+nrecord iff (A,B: CProp) : CProp ≝
+ { if: A → B;
+   fi: B → A
+ }.
+
+notation > "hvbox(a break \liff b)"
+  left associative with precedence 25
+for @{ 'iff $a $b }.
+
+notation "hvbox(a break \leftrightarrow b)"
+  left associative with precedence 25
+for @{ 'iff $a $b }.
+
+interpretation "logical iff" 'iff x y = (iff x y).