-definition empty2nat : empty \to nat \def
- \lambda x : empty . S (match x in empty with []).
\ No newline at end of file
+inductive empty (x:nat) : nat \to Set \def .
+
+definition empty2nat : (empty O O) \to nat \def
+ \lambda x : (empty O O). S (match x in empty with []).
+
+inductive le (n:nat) : nat \to Prop \def
+ | le_n : le n n
+ | le_S : \forall m:nat. le n m \to le n (S m).
+
+inductive True : Prop \def
+ I : True.
+
+definition r : True \def
+ match (le_n O) with
+ [ le_n \Rightarrow I
+ | (le_S y p') \Rightarrow I ].
+
+inductive Prod (A,B:Set): Set \def
+pair : A \to B \to Prod A B.
+
+definition fst : \forall A,B:Set. (Prod A B) \to A \def
+\lambda A,B:Set. \lambda p:(Prod A B). match p with
+[(pair a b) \Rightarrow a].