+
+theorem t: let f \def \lambda x,y. x y in f (\lambda x.S x) O = S O.
+ intros. simplify. change in \vdash (? ? (? %) ?) with O.
+ reflexivity. qed.
+
+theorem X: \forall x:nat. let myplus \def plus x in myplus (S O) = S x.
+ intros. simplify. change in \vdash (? ? (% ?) ?) with plus x.
+ rewrite > plus_comm. reflexivity. qed.
+
+theorem R: \forall x:nat. let uno \def x + O in S O + uno = 1 + x.
+ intros. simplify.
+ change in \vdash (? ? (? %) ?) with x + O.
+ rewrite > plus_comm. reflexivity. qed.
+